If you're one of those people who quite likes computer games but finds the endless mayhem and slaughter a bit unseemly, there is another option: putting imaginary things on top of other imaginary things. At your leisure. Does that sound sufficiently exciting?

Well, Minecraft allows you to do just that; it may have been billed as the "coolest game you've never heard of", but it has about as much in common with Call Of Duty or Angry Birds as hopscotch or basket weaving.

There are no scores, no obvious goals to aim for, no point at which you can punch the air and say that you've triumphed; you simply move around a randomly and dynamically generated world, collecting objects and building things.

The pace is fairly docile, the graphics retro and rudimentary, the environment consisting almost entirely of cubes to be prodded, picked up and rearranged. But despite its lack of va-va-voom, Minecraft has become an online sensation and its creator, Markus "Notch" Persson, has become an unlikely hero of the gaming fraternity.

So what is its curious appeal? "Lego enthusiasts have a term 'the dark ages' to describe the time between abandoning Lego as a child and taking it up again as an adult," Alan Miller, a keen gamer, says. "And I think that same rediscovery of creation has driven much of Minecraft 's success." The idea behind Minecraft certainly hasn't sprung from nowhere; much of Persson's inspiration came directly from a PC game called Infiniminer and the comparisons between the two are immediately obvious.

But Minecraft synthesises a number of gaming heritages, according to Margaret Robertson, development director at the game-design company Hide & Seek: "It pulls things together from world-building games – where you sculpt the terrain – but also a certain type of role-playing game where your progress depends on finding and collecting items."

The comparisons with Lego have provoked a debate over whether Minecraft is even a game at all; maybe it should be considered more as a lowly "toy"? But when the sun sets over your Minecraft world every hour or so and darkness creeps in, monsters (or "mobs") emerge – and if you're not tucked up safely within your construction, your game may well be swiftly curtailed. "That makes it very different from playing Lego," Robertson says. "If you could do anything in Minecraft, if you could make anything you like with infinitely powerful tools, it would get boring quite quickly. And if you failed to achieve something magnificent, you'd have no one to blame but yourself. But by being threatened by the things around you, Minecraft makes your accomplishments feel far more impressive. It's definitely a game."

But what exactly do you accomplish playing Minecraft? Head over to YouTube, where home-produced videos of Minecraft creations litter the top 10 most popular videos each month, and you'll find such delights as a 1:1 scale model of the USS Enterprise, rollercoasters, reconstructions of the Titanic and much else.

"I think of it as this generation's equivalent of dad tinkering in the garden shed," Miller says. "He has some wood, he's knocking nails in, you have no idea what the hell he's doing out there, but he's making something. And it's that same impulse going on in Minecraft."

But Robertson sees the inherent vagueness of the game causing it to mean different things to different people. "There are two distinct tribes within Minecraft – the builders and the explorers," she says. "I'm not a builder; my house in Minecraft is five blocks of dirt with a bed on top. In the 'morning' I get up, put my bed in my pocket and head out to see what I can find – and it's that sense of exploration that I love. I'm literally exploring terrain that no one has ever seen before and I'm amazed at how enduring and exciting I find that."

If you read that and question whether Robertson needs to get out and explore the real world a bit more, you're not alone. Minecraft has been criticised as a "game for gamers" and many believe that it can only be appreciated by those already immersed in the world of computer games.

"It definitely feels as if there's an ownership of it by the gaming fraternity," David Ramsden, a Minecraft fan and games-design student, says. "Because there's a steep learning curve and the game doesn't hold your hand in the initial stages, it feels like 'our' thing. We're the ones who've created an online wiki that guides you through it, for example. Also, Minecraft feels like an anti-corporate game – one that isn't like every other game that's out there."

Minecraft has achieved great success on a tiny initial budget; more than three million copies have been sold so far, with publicity coming entirely via word of mouth and social media.

"It's amazing for an independent game," Jane Douglas, at GameSpot UK, says. "The giant blockbuster games sell many times that amount, but it's still hugely impressive. It's created by one guy, developed by a very small team, but has had more than 12 million people register to try it out for free. And it's remarkable in turn than a quarter of those people went on to pay for the full version." Minecraft, currently available for PC, Mac and to play in a web browser, has been in constant development since its quiet launch in May 2009, but will have a proper release in November, when there will also be the first MineCon conference – in which enthusiasts will gather at Las Vegas's Mandalay Bay hotel for two nights to discuss the game.

That also coincides with a release for iOS (Apple's touchscreen products) and Android, Google's mobile operating system, along with a convention in Las Vegas. But will the world embrace Minecraft in the same way that gaming enthusiasts have? Robertson believes so. "I've heard an awful lot of stories of families who play Minecraft together," she says. "There are also many people who don't like the way conventional console games are going at the moment who really like Minecraft and I think the sales figures show that it's reached beyond the nerds."

Curiously, for a game that's predominantly a single-player experience, it has brought players together into enthusiastic communities – which explains much of the viral spread of the game.

"If you struggle with it on your own, you talk to other people about it," Robertson says. "That steep learning curve is a high-risk strategy for games to pursue, but in this instance it has absolutely worked. It's a game about communication."

And it is a game about addiction. Once you've battled your way through the initial stages, the unrealistic vistas of Minecraft are compelling. "You come across a new island with some materials that you haven't used before," Ramsden says. "And suddenly there's this rush of excitement: what can I make with that? It's peculiar how these things hold an appeal within a gaming environment. I can't build a skyscraper in real life, with my own hands. But I can in Minecraft."

Robertson's love of the game is similarly undiminished and her respect for Persson is huge. "Because he's such a sweetheart and very avuncular, he is often accused of being lucky rather than talented, but that's nonsense," she says. "He's very astute, very clever, and very savvy in the way he talks to his community and learns from them. And the game – I'm still enthralled by it, the way it keeps me chasing things I've never seen before."

Low-budget games gone big

World Of Goo

From a budget of just $10,000 (£6,400), the San Francisco-based independent games studio 2D Boy created this cartoon-coloured creation. The game involves building structures out of googly eyed goo-blobs, in order to lead as many blobs up a drain pipe to safety.

Paper Plane

A winner of the 2011 student showcase award at the Independent Games Festival, Paper Plane has a decisively melancholic feel to it, as you fly through a landscape of childhood memories.

Fez

A beautifully designed platform game, which defies dimensions as you revolve the entire world around you to explore in 3D. Produced by the slick independent software developers Polytron, the game features plenty of MC Escher-like optical illusions to keep you guessing.

Stepmania

Until the Nintendo Wii emerged, dancemat games were perhaps the only redeeming feature of an industry determined to keep people stationary. Stepmania takes it back to the office chair as your fingers do the "dancing".

Crayon Physics Deluxe

Another IGF Awards Grand Prize Winner, Crayon Physics is a world where 2D scribblings on a piece of faded paper take on actual physical properties. What looks like the drawings of a toddler are the makings of a complicated puzzle game.