You've finished The Wire box set? You'd like something else that is just as good as "the greatest show ever in the history of television" (© all Guardian journalists) but you're not quite sure where to go next? How about a series that's as passionate and intelligent as The West Wing when debating war and terrorism, or as emotionally articulate about death, loss and love as Six Feet Under, or as trippy, mystical and deliciously baffling as Twin Peaks? A series that's not afraid to take you on an epic, existential journey during which you'll grow to love characters who are wrangling with metaphysical issues such as the nature of humanity and god? A series that does all this while never losing sight of the idea that television should be entertaining? But what's that? You don't do spaceships? Oh ...

That's the problem when you start to recommend Battlestar Galactica. As we approach the last-ever episode (or get ready for the last box set, depending on how you're watching it), it's clear to fans that the last five years have been about much, much more than watching robots chasing people across space. And yet, there's no denying it - BSG is filled with scenes where brilliant actors such as Mary McDonnell or Edward James Olmos are called on to deliver lines about "firing up the FTL drives for a jump" with a straight face.

And yes, it is set in a universe where a lone military spaceship is protecting an ever-dwindling population of humans from the relentless onslaught of a race of sentient robots. And yes, even the show's name is ridiculous. It's not solid and enigmatic like The Wire, it doesn't have the elegant irony of The Sopranos, and there's a distinct lack of the now-wow zeitgesty zip you get from say, Sex and the City or Desperate Housewives. It's daft. It's pompous. It's - let's face it - sci-fi.

And yet, as anyone who has actually committed to it will tell you, BSG has evolved into one of the most sophisticated, compelling and original shows that's ever been made. Which isn't bad for the remake of what was in itself a trashy show - one designed chiefly to cash in on the success of Star Wars. If you were a kid in the late 70s/early 80s and found yourself plonked in front of the TV on a Saturday night, you might remember watching Lorne Greene hamming it up in the original Battlestar Galactica while his ace fighter pilots Dirk Benedict and Richard Hatch fended off evil "cylon" robots every week.

The new version of the show that emerged in 2004, courtesy of producers Ronald D Moore and David Eick, might have shared the bare bones of creator Glen Larson's original space-western - the plot and the character names, and also Richard Hatch (playing a terrorist-turned-politician in the reboot) - but that's about all.

The cylons in the new version still appear as hulking metallic "centurions" similar to the ones in the 80s (except now they're equipped with machine-gun hands), but the cyclons to take note of are the models who have somehow evolved to look exactly like humans. For reasons that may or may not be related to the show's budget, the cylons have only managed to clone 12 different human models, so the vast ranks of cyclons are all played by the same 12 actors. (That may sound confusing, but it's not a patch on how confusing BSG will seem to you if you casually dip in to an episode without starting the show right from the beginning.) As the new show begins, these human-lookalike models are the enemy within, living in secret among the humans - some undercover, but some, who have not yet been activated, with no idea that they are machines.

What really sets the show apart from the original, though, are its politics. With an opening that starts with an apocalypse - the near wiping out of the human race by the cylons - and ratchets the action up from there, it's hard not to read the series as being anything other than deeply rooted in the politics of Bush-era America. The idea to revive the show came shortly after 9/11, and its influence permeates the story. But where a contemporary show such as 24 has chosen to deal with the war on terror by setting up a string of impossibly last-minute disaster scenarios that can only be foiled if Jack Bauer flicks through his on-the-hoof torture manual, Battlestar has taken a much more elegant and complicated tack.

At first, we sympathise with the humans (read: America), under attack from a horde of impossible-to-detect alien invaders within (read: al-Qaida). Then you realise that it's the cylons, the baddies, who believe in a more Christian-sounding "one true God" - and the humans who worship a bunch of different gods. And that even though they've perpetrated mass genocide, it's nonetheless the cylons - created and then turned upon by humans - who believe themselves to hold the moral high ground.

In its third series Battlestar manages to pull off one of the most extraordinary leaps in American TV when the surviving group of humans find themselves living under cylon occupation on a new planet and our human heroes decide to use suicide bombing against the cylons. It's the sort of move you can only pull once you've taken viewers with you on a properly engaging journey. Suddenly you're looking at a collection of people that you've come to know and respect - rather than a string of dramatic archetypes - and being asked to watch them, even identify with them, as they debate the merits of terrorism. So it's Colonel Tigh, the brilliant, bitter, drunken military man, who decides to sacrifice innocent human bystanders for the sake of taking down a few "frakking toasters" (as they call cylons).

Even if you don't agree with their actions (and the show's not so glib that you're supposed to), you understand how they've come to them, and that's the key to BSG's genius. It doesn't ever talk down to its audience, or pander to gung-ho-American-war-on-terror rhetoric. Instead, it plays out issues in an adult fashion, allowing characters to debate what they're doing, to remember what they've done, to question why they're doing it - and crucially, to be called to account for their actions later. It's this sense of time passing and actions being remembered that gives the show a real depth. Characters grow, change their minds, fall in and out of love, quit jobs and get arrested, lose themselves in drink binges and then pull themselves together.

It's also a show that's technically very much of its time , with people devouring it on Sky1's HD broadcasts days after US transmission, nicking it off PirateBay to watch on laptops just hours later, downloading it legally from iTunes - or waiting for the box sets, where it makes the perfect "just one more" experience. But all that's also served to diminish the impact to some extent. Even with fellow fans who you know are watching on the same format as you, it feels only polite to start every conversation you want to have with, "Hang on - where are you up to?" just to make sure you don't blow any crucial new moments. Like so many of the best shows to come out of America recently (The Wire, Breaking Bad, 30 Rock), its reception has been one of a slow groundswell, rather than an instant mass hit. It's one of those quirky, modern life conundrums. You want to tell as many people as possible that they're missing out on something really special, but you don't want to tell them too much in case they do end up watching it; or even talk about it too loudly in public because you can't really keep prefacing every conversation you'd like to have over the water cooler with a verbal spoiler alert just in case you ruin anything for anyone within earshot who is keeping up. (This is also the reason why I'm avoiding details about the final series here, as a lot of fans are waiting for the final DVD. But it's good. Really good.)

If you're still not convinced you should give it a go, maybe we should leave it to the succinct words of the great amazon.co.uk poet who wrote: "If you liked that other great stuff, you'll like this."

The key players

(Spoiler alert: if you haven't watched any of the shows, don't read this)

Dr Gaius Baltar (James Callis)

Baltar starts out as the galaxy's smartest (human) scientist. Then he is seduced by an enigmatic woman, who is actually Caprica Six, a cylon agent on a mission to gain access to humans' defence mainframe. When the cylon nukes start raining down, Baltar realises he has inadvertently betrayed his entire species. Baltar survives the nuclear holocaust and his subsequent journey through space takes him from trusted scientist to vice-president, then president, war criminal, cylon prisoner and finally religious cult leader. All through the series he sees visions of Caprica Six in his head that are never really explained. Is she a ghost? An angel? A cylon chip implanted in his head? Or is he mad? Whatever the truth, Callis's performance is extraordinary.

Number Six (Tricia Helfer)

Of all the humanoid cylons, it's the Number Six model we see in the widest number of roles. First, there's the Six on the planet Caprica who convinces Baltar to hand over the defence codes. Then there's the model who shows up early on to try and denounce Baltar as a traitor. Another version of Six is stationed on the Battlestar Pegasus and has a relationship with Admiral Helena Cain before betraying her. Other models look after Baltar on the "cylon basestar" and run the occupation government on New Caprica. Sixes are everywhere. And it's a testament to Helfer's excellent acting that they all seem so different. Oh, and she looks amazing

President Laura Roslin (Mary McDonnell)

Laura Roslin is education minister - and 43rd in line to the presidency - when the cylons first attack. The next moment, she is president. It is not exactly a resounding triumph for democracy, but she soon rises to the challenge. Later, the drugs that she is taking to counter the effects of her breast cancer treatment give her hallucinations that convince her that she is the "dying leader" who is destined to lead the fleet in search of Earth in an ancient religious prophecy. And yes, in the future, it would seem, breast cancer is still a threat. And people (particularly doctors) still smoke cigarettes.

Kara "Starbuck" Thrace (Katee Sackhoff)

She starts out as the fleet's most skilled pilot (in a role played by a man in the original show) and ends up as its "harbinger of doom": Starbuck has definitely had one of the more unusual story arcs during the series. After a long will-they-won't-they relationship with Lee Adama, the son of Battlestar Galactic's commander, she gets married to someone who turns out to be one of the Final Five Cylons - which, of course, won't mean anything until you watch the show. Along the way she is brainwashed by various copies of a certain cylon (whom she keeps killing), seems to die in an explosion in space, and then somehow turns up in a new ship with the directions to Earth. Go Kara.

• The final episode of Battlestar Galactic is on Sky1 on Tuesday 24 March at 9pm.