A millionaire in his thirties, Charles Veley decided he wanted to "go everywhere". Ten years on, he has visited 806 of 871 "countries" and is looking to complete the set. Tim Adams joins him in Heligoland to find out why he has to keep moving

One of the things Charles Veley, the world's most-travelled man, has discovered is that there is always a bar. There was a bar on Palmyra Atoll, south west of Hawaii (population: 8); there was a bar on Willis Island in the Coral Sea, off the coast of Queensland (population: 4). Ten minutes after he and I have arrived in Heligoland (population: a few hundred frozen Germans, and us) we are, therefore, sitting in a one-roomed pub, advertised by a gigantic wooden herring outside, and crammed inside with Dutch and German and English nautical knick-knackery. It is midday, and we have been on the road for four hours: first by car from Hamburg through fog and a blizzard to an airstrip at Uetersen. Then by eight-seater plane, which took off in a perturbing foot of snow, to an island called Dune. Then by roiling ferry across to here, Heligoland, holy land. It feels something like a pilgrimage for the insane and the desperate, and Veley, a neatly groomed, 44-year-old American, has been on the lookout for signs and wonders.

"This is part of my style," he tells me, gesturing around the bar. "Heligoland: I had no idea about it. So when we got here I waited for something. I saw this piece of paper in the window saying Eiergrog – "Egg grog" – and it looked interesting, so I walked past the big wooden fish and came in. My philosophy for travel is this: always plan as if you are going to do a Japanese-style tour and every second is accounted for. But on arrival, abandon all that and do whatever feels right. Eiergrog felt right. And you walk in, there is a pretty girl behind the bar, and you start to understand the place."

Iris, the pretty girl, has just placed two Eiergrogs on the table in front of us: hot, rum-based, raw-egg drinks whisked into a froth. Iris came here six years ago to do a seasonal job from Berlin, met a man, and stayed. "It is," she says, nodding at the swirling snow outside, the boarded-up beach huts and shop fronts, "better in summer." She has now met another man and plans to follow him to Australia. There is one other drinker in the bar, an 87-year-old named Herr Westerhaus, sipping glasses of hot gin. He has a daughter in East Anglia and was, he says, a radio signaller here for U-boats during the war. He had so many good memories he came back when he retired.

Veley, who slips easily in and out of German, has stories for both Iris and Herr Westerhaus; he has been to all the places they have been. In fact, as it quickly becomes apparent, he has been to all the places anyone has been. Heligoland is number 806 on Veley's list of visited "countries". He ticked off all the 193 UN-recognised nations eight years ago, and since then he has been collecting islands and atolls, provinces and protectorates. These days he runs a website called Most Traveled People, which has 8,000 members, mostly, like him, "competitive travellers", trading stories about Mizoram, Kingman Reef and Rio Muni. He established it, he suggests, in an attempt to bring some rigour to these travellers' tales, to rationalise the globe's possibilities (and, you imagine, to advertise his own unprecedented wanderlust).

It hasn't, he concedes, always worked out like that. The world of competitive travelling is, well, nothing if not competitive. For a start, deciding what is and what isn't a separate "country" – "a discrete geographical, ethnological or political entity" – threatens to become almost a full-time job in itself. Border disputes are rife. "People put forward nominations and I collect those," he says. "And whatever has the most nominations becomes a candidate, and then there is a voting process. Spain and France and Italy and several others are now divided into semi-autonomous regions. So it's getting tougher…" He doubts anyone, not even himself, will ever get the whole list (which currently stands at 871). "We are always adding new places. And there are already some really difficult places out there. Like Scott Island, a New Zealand island toward Antarctica; only six people have ever landed on it." He says this with a certain frustration.

Beyond the attempt to quantify all the world's remotest corners, there are also ongoing qualitative arguments, mostly about what is meant by the word "visit". Some travellers claim you must spend a night in a place; some argue it is enough to visit a lavatory there; "others," Veley suggests, somewhat wearily, "will say you have to sleep on a park bench or do it for less than $10 to make it real. And some people believe you must have cocktails at Annabelle's or wherever…" Veley has attempted to bring some order to this area, too. Just touching down while on a plane is not enough; Most Traveled People requires a photograph or a passport stamp or a credit card receipt. He recently, he says, personally defined the minimum requirements of what constitutes a "landing" on the North Sea island of Rockall (of shipping forecast fame).

He'd had a go at Rockall once before, with his friend, the clubbable castaway Ben Fogle, but the weather had been too tricky and they had turned their sailboat back. This time, with a different group, he set off from Benbecula, and it was beautiful, calm sailing for two days. When they got to Rockall, however, even in those perfect conditions, it was not clear exactly how they might land. "The swell is 7 metres, maybe," Veley recalls, "and the rock has sheer sides all round with powerful eddies beneath them." Veley and his fellow travellers circled the rock for half a day, waiting for a change in the sea. "We eventually decided to have a go at one corner that was a bit more craggy and had a skirt of thick kelp attached to it," he says. Among the crew was a photographer from Stornoway, who donned a wetsuit and jumped on a surfboard. "He timed the swell, grabbed the kelp, found the crag and hauled himself up," Veley says, "and we were all cheering wildly." Then it was Veley's turn. It took him ages to get the wetsuit on. The swell seemed even wilder. He plunged in. "I found the kelp, timed the surge, grabbed the crag, stood up on Rockall for maybe one and a half seconds before the next wave crashed over and knocked me straight back into the sea. But that counts, for sure…"

We order two more Eiergrogs.

Charles Veley grew up in Brooklyn and never left the United States until he was 18. His parents split up when he was young; money was tight and didn't extend to foreign holidays. Veley recalls sitting as a boy in the driver's seat of his father's car with the Rand McNally map on his knees, planning trips from coast to coast in his head, imagining himself always on the open road.

His first attempts at escape came when he was sponsored through his computer science degree at Harvard by the Officer Training Corps of the US Air Force; this was the era of Top Gun and competition for places was intense. Veley topped his year as a trainee fighter pilot before being abruptly dropped from the programme when a routine medical discovered a minute scar on his retina. By that time he was pulling jets out of tailspins and imagining 10 years stationed in remote air bases.

He responded to the disappointment by taking a flight over to the UK to see some friends at Cambridge, and from there his addiction to travel began. He took a Eurail pass and was hooked by the possibility. The last time he was in this part of Germany he got off at Hamburg train station and went running round town trying to eat a hamburger. "I had never left the States and suddenly there were borders, passport stamps..." Romance was a part of it, the prospect of unexpected encounters. "I had a three-week coach pass around Britain, too," he recalls. "I really wanted to go to Dorset because I loved Thomas Hardy, and I wanted to go to Scotland. I remember being in this overnight coach from Birmingham up to the Highlands and there was this redheaded girl sitting next to me. And I remember sort of in the middle of the night we were snogging suddenly. I had a lot of interesting seat mates on coaches."

When he returned to the States, Veley joined with some friends in setting up a dot.com company creating software that delivered business intelligence, helping retailers to understand the buying patterns of consumers. He worked 100-hour weeks and managed some long-haul travel when he could. In 1999 the company, MicroStrategy, floated on the ballooning Nasdaq and the share price peaked at $333. Veley had 500,000 shares. He was about to get married, he was 35, and he decided to retire.

"I'd always had a goal to speak five languages," he says. "I was studying French, German and Italian at night school, and then I thought: why do this? Why not go and live in these places instead? So my wife Kimberly and I went and did a year abroad – this was 2000. We got two round-the-world tickets and we lived in France and then Germany and then we went down to South Africa, and the geography down there just blew my mind. I realised we could go to Malawi, Botswana. And then we took another year and went to South America. And then I learned about the Travelers' Century Club, which has an entry level of 100 countries." At the same time he was getting more and more interested in round-the-world tickets. "If you really get into the mechanics of them," he says, "you can fly first or business and pay much less than economy, and that appealed to the computer side of me, puzzling over algorithms."

Along the way, while he was in Tasmania, Veley discovered by turning on the TV that he was no longer a multimillionaire: the MicroStrategy share price had crashed to 40 cents, but he was too far gone in his travelling to turn back. He figured the shares would bounce back. He booked some more flights. It was when he and his wife were on the way to Hong Kong from Korea and he became excited when he realised they could stop in Taiwan for four hours that he knew he was hooked.

For a few years after that Veley averaged around 100 countries per year. Some trips were more efficient than others. He flew to the South Pole in 2003 and took in Argentinian, Australian, British, Chilean, French, New Zealand and Norwegian territories without leaving the same spot – all countries disputing a single patch of land. The share price did rally somewhat, and he spent, he reckons, more than $1m on plane tickets and freighter passages and sailboat charters: 1m miles of travel in just three years, which took in every place you could name, and plenty you couldn't: Malyj Vysotskij Island, Zil Elwannyen Sesel, Ogasawara.

For much of that time, Veley's wife accompanied him, clocking up 200 countries herself, but in 2004 they had their first child, and now they have three, aged six, four and two, all autumn births because the Antarctic exploration season ends in February, and by that time Veley had generally been away from home for more than three months. He insists that since his children have been born family has been his priority, but he still pursues his impossible itinerary. When we meet he is midway through a 16-stop round-the-world ticket, en route home for a week in San Francisco to catch the end of Valentine's Day and take the children off to Disneyland. Then he has a province of Argentina to collect.

Veley is telling me all of this while we wander somewhat aimlessly in the sleet and knifing cold, fortified by Eiergrog, up to the high point of Heligoland, past a stark geometric church to a headland spiked with radio masts and overlooking rock stacks washed by the ocean. He takes it all in without too much comment. He doesn't collect souvenirs, or take photos beyond the odd snap on his iPhone, or jot down notes. Never does.

I'm intrigued, of course, by his motivation, but he can't explain the obsession much except in the blandest terms – proof positive that you are either a psychologist or an adventurer, but rarely both. "If you want to have a complete worldview you have to go everywhere," he'll say. "Every place you learn something new." Or: "It's an investment in life experience. Whenever I meet anyone, no matter where they are from, I can always relate to them." Or: "While I'm alive I just want to see as much of the world as I can. I'm organised; I have a computer background." When I mention the environmental impact of his travels, he brushes the question aside. "I care about the environment just like you," he says.

The challenge itself is sometimes enough of a motivation. Palmyra Atoll (population: 8; bars: 1) is maintained by Nature Conservancy in the US. In his enquiries about how he might get there, Veley was referred to a woman named Nancy at the Conservancy offices in Vermont. She suggested to him that the only people who ever got to go to Palmyra Atoll were those who made at least a "six-figure contribution to Nature Conservancy". To Veley this was fighting talk. "I can be quite persistent," he says, on deserted Heligoland, with a degree of understatement. In the end he chartered a boat out of Hawaii with a few others to share the cost. "We finally arrived at Palmyra some days later," he recalls. "The bar is a run-down wooden structure built 30 years ago and yachties had written stuff on the walls. I wrote a 'Poem to Nancy': 'Palmyra is nice/great palm trees and sand/please lower the price/from one hundred grand…'"

It seems almost redundant to ask Veley about his favourite places, though from time to time – he has a weirdly accurate memory for names and events – he will suggest how he had a fine time on St Kilda, or he'll let slip that everyone loves country and western music on Pitcairn. The strangest place he's ever been was the "conference room" between North and South Korea, in Panmunjom, two nations staring at each other. The scariest: Afghanistan on the first anniversary of 9/11. He once made a list of all the worst things that had happened to him: the time a tree frog urinated on his forehead in Tortuguero, or when his canoe capsized in the Zambezi, among hippos, or when he waited for three days for a boat out of Christmas Island, and when it arrived he went to introduce himself to the captain before their 1,000-mile voyage only to discover him drunk, stoned, naked and masturbating in his cabin.

The urge to travel to Veley's extent, a kind of attention deficit on a global scale, has a medical diagnosis: dromomania, the addiction to new experiences, the vagabond neurosis. He's a curious case, though. While most dromomaniacs are permanently wedded to the road, Veley is both rooted and adrift, very settled, he insists, and almost permanently travelling.

His rivals – nearly all of them acquaintances – have sometimes claimed that what Veley does is not really travel at all: it's too systematic, there's no depth to it, not enough danger. He became friendly with John Clouse, who for many years was the Guinness world record holder as the most travelled man (before Guinness decided to abandon the category, as there were too many conflicting criteria). Clouse, a lawyer from Indiana, went through six marriages before his death two years ago at 82. "He tended to find a new wife and travel with her, and then she would realise what was involved," Veley explains.

About three-quarters of the travellers on his website are men, though the "leaderboard" used to include a woman who claimed all sorts of incredible journeys. She had claimed, for example, that she had been to Mount Athos, the Greek monastic state into which only males are allowed, arguing that when she was a girl her father had cut her hair short and taken her in. Veley asked for proof of some of her exploits and she immediately removed herself. The table currently shows a man named Bill Altaffer slightly ahead of Veley, but though Veley doesn't doubt Altaffer's "been all over the place" he suggests that Altaffer refuses to always provide the evidence required, and that their paths don't cross too often, and "it is, I guess," Veley says, "not worth worrying too much about".

One of the things that his years of waiting for planes and boats has taught him is that, try as you might, you can't force situations. "I remember on my initial Euro trip it was late afternoon and I was in Rome and I couldn't go in the Vatican because I was wearing shorts. I remember thinking: this is the only chance I will ever have. I was wrong." The first time he tried to get to the North Pole on an icebreaker from Svalbard they got stuck in the ice at 86 and a quarter degrees latitude. He went back the next year and made it. "Things will come round again" is his mantra. His only assets, he suggests – beyond, that is, his financial resources – are patience and politeness in negotiating the world's officialdom. To that I would add a certain sure sense of restlessness, of giving the impression of being on the way somewhere else, of nowhere being a final destination.

On the boat back to the airstrip on Dune we find ourselves in the cabin of the Heligoland ferry with half a dozen German men in their sixties, who appear to have been at the Eiergrog all day. Discovering we speak English they launch into a rousing version of "What Shall We Do with the Drunken Sailor" as the small boat pitches across the bay. They come here every year, one of the more sober members of the group explains to me as we approach the airstrip. Have been doing so for 40 years, always this weekend in February, always this place. "Nothing changes. Friends, the same. Heligoland, the same. That's how we like it," he says. Charles Veley joins in with the singing, files away the experience neatly, but I'm guessing he is also planning what to do later in Hamburg, and thinking about tomorrow morning's flight, and the one after, and the one after that. Novelty can have its own monotony, too.

Charles Veley's top tips



Favourite all-round destination: Lord Howe Island (370 miles east of Australia)

Favourite country: I love them all

Best cuisine: Thai

Worst cuisine: Turkmenistan

Favourite bar: Hemingway Hotel Ritz, Paris

Favourite airline: Singapore for long-haul; Virgin America for domestic

Best airport: Hong Kong

Secret to beating jet lag: Travel westwards

Most underrated tourist attraction: most World Heritage Sites

Most overrated tourist attraction: South of France in August

Best beach: Anywhere on the north shore of Kauai, Hawaii