Continuity. Character arcs. Sub-plots and cliffhangers. They’re the bones on which a lot of great TV’s draped - the elements that have us rushing back to our favourite shows week after week, whether it’s House Of Cards, Attack On Titan or Agents Of S.H.I.E.L.D.

But can a TV show blithely shun things like continuity and recognisable character arcs and still provide something reliably amusing, thrilling, even moving? Space Dandy, the animated series from Cowboy Bebop and Samurai Shamploo director Shinichiro Watanabe, plays fast and loose with the episodic TV format, frequently giving continuity short shrift, yet the result is one of the most fascinating anime shows I’ve seen in years.

To quote the opening credits sequence, Space Dandy is a dandy in space: a preening, lecherous oaf who roams the galaxy in his ramshackle, Hawaiian-themed ship (the Aloha Oe) in search of undiscovered alien life. Far from a curious adventurer, Dandy’s essentially a bounty hunter; the aliens he finds are dragged back to a space station where they’re registered in exchange for cash. Most of the time, Dandy prefers to hang out at a Hooters-like restaurant called Boobies, ogling the scantily-clad waitresses and making a cup of coffee last as long as he possibly can.

Dandy’s another in a long line of lovable rogues with a space ship; in his DNA you can see distinct traces of Han Solo, plus a splash of Zapp Brannigan’s misplaced self-confidence, Peter Quill’s likeable clumsiness and, to cite a character outside the sci-fi genre, the Fonz’s penchant for styling cream.

Like any astro-rogue worth his salt, Dandy has a couple of colourful sidekicks. The first is QT, a studios, sweet-natured robot Dandy bought in a thrift store in the hope of gaining his own R2D2, but who instead turns out to be an old cleaning droid with out-of-date system software. The second is Meow, a feline alien from the planet Betelgeuse who Dandy initially mis-identifies as an unregistered species. Clambering aboard the Aloha Oe with claims that he can point Dandy in the direction of some real undiscovered aliens, Meow joins QT as another of the hero’s longsuffering compatriots.

Far from a pure space opera series, Space Dandy has the free-wheeling, cynical tone of John Carpenter’s Dark Star. There are long scenes where the central trio simply lounge around the ship, alternately getting on each other’s nerves or quietly reading adult magazines. The second episode is devoted to the quest for a decent bowl of ramen.

But at the same time, Space Dandy also functions magnificently as pure sci-fi. Freed from the shackles of cliffhangers and series continuity, the series veers wildly from one location and to the next in each episode, with the animation style often changing to reflect the story’s themes. Some of the aliens Dandy encounters are truly alien; a planet populated exclusively by sentient plants has a woozy, psychedelic quality. Another alien is able to transfer the consciousness of other characters into inanimate stuffed toys.

Gradually, however, common threads start to appear between each episode. There’s the mysterious Gogol empire, and an ape-like character called Dr Gel, that follows Dandy all around the universe. At first, their inability to catch Dandy - and Dandy’s complete obliviousness to their existence - seems like nothing more like a disposable running joke, but their presence begins to make more sense towards the very end of the second season.

Dr Gel’s ship aptly sums up Space Dandy’s mix of weird humour and sci-fi savvy cleverness. It’s essentially the head of the Statue of Liberty with thrusters attached to the back. The statue also has a gigantic ball gag in its mouth, like the ones in Pulp Fiction. Is the ape-like Dr Gel and his chosen transport an irreverent homage to Planet Of The Apes?

Episodes freely reference everything from 80s videogames (Galaga’s a regular touchstone) to Groundhog Day to old Japanese henshin mecha shows. There’s a febrile, fizzy tone to Space Dandy’s references and ideas, with brilliant concepts introduced, toyed with for a few minutes and cast aside for good. Initially, the show’s mix of comedy, retro-stylings and self-contained stories might make it seem as shallow as Dandy himself, yet the series continues to introduce hidden depths.

In its latter stages, the series explains why events in one episode appear to have no bearing over those in the next. Series two’s finale unexpectedly wraps things up in a way that ingeniously explains everything from the motivations of the Gogol empire to the identity of the wry, Hitchhiker’s Guide-like narrator who comments on each episode.

It would be remiss not to mention that Space Dandy also looks and sounds brilliant. The animation, a lively mix of CG and hand-drawn 2D, is both redolent of 70s and 80s anime and utterly fresh, while the music - a mix of electronica and funk - is simultaneously cheesy and unspeakably cool.

Most of all, Space Dandy works because its characters are so immediately likeable. They don’t necessarily have arcs as such, in that they change as the two seasons go on, but each episode subtly fleshes out each character - Dandy’s gradually revealed to be (slightly) less of a brainless oaf, while an episode in which QT falls in love with a coffee machine proves to be far more affecting than it sounds. Even incidental ones like Honey, a waitress with a complex past, or Bea, a seemingly frivolous underling who serves Dr Gel, prove to be far less one-dimensional than they first appear.

Space Dandy originally aired in US and Japan last year, but it’s now on UK Netflix. I can’t recall another animated series that I’ve devoured quite as quickly as this one. Whether there’ll be a third series, as hinted at the end of the season two finale, isn’t yet clear. But even if there isn’t, the 26 episodes that make up the current Space Dandy saga are damn near perfect.

Like Dandy himself, the show seems shallow at first glance, yet each episode reveals more depth and intelligence. It’s tough to choose just five essential episodes from the 26, but for me, the following represent the very best Space Dandy has to offer.

An early example of just how flexible the Space Dandy format is. One by one, the crew of the Aloha Oe are infected by a zombie virus. As the entire universe gradually becomes a shuffling, dribbling ghoul, the episode dares to suggest that zombification could represent a kind of liberation - no more work, no more war, and so forth - and the entire show is peppered with references to George A Romero movies and other classic works of zombie horror.

The Lonely Pooch Planet, Baby (series 1 episode

Dandy stumbles on a planet comprising of little more than the shattered remains of ancient space craft, before finding an adorable dog among the wreckage. The pooch turns out to be none other than Laika, the first dog in space. It’s a delightful, moving episode, and also very funny - witness, for instance, Meow’s initial jealousy at Laika and Dandy’s friendship.

A time-loop episode based on Groundhog Day’s concept, There’s Always Tomorrow, Baby makes the idea its own. Witness, for example, how long it takes for Dandy, QT and Meow to even notice that they’re living through the same day over and over again. They’re so content to simply sit in a bar drinking that it’sabout three months before they even notice that anything’s wrong. Like just about every episode of Space Dandy, there’s also something deeper going on here; the time loop planet is Meow’s original home, which resembles an economically ravaged part of modern-day Japan. The episode exemplifies how effortlessly Space Dandy’s writers can weave humour and thought-provoking sci-fi.

Here’s an episode that shows off some of Space Dandy’s great animation. Alternate versions of Dandy, Meow and QT emerge from different dimensions, allowing the animators to go wild with variations on their character designs which freely reference dozens of other shows.

Dazzlingly imaginative, this episode sees our three-dimensional reality suddenly visited by a two-dimensional reality, which sucks everything that touches into it and turns them into flat objects like something out of an old videogame. Once again, Space Dandy takes a seemingly nonsensical subject and gives it a warped internal logic; the appearance of the 2D universe has something to do with a jealous prince, and an old girlfriend of Dandy’s who happens to be a four-dimensional being.

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Those are just five great episodes from Space Dandy, but there are so many other great ones. What about The War Of The Undies And The Vests, Baby, which is the kind of weird satire that could have been written by Jonathan Swift? Or the episode where Dandy’s challenged to a space race, and there’s a foul-mouthed lawyer rodent who appears to be a parody of Mickey Mouse?

While not every episode of Space Dandy is perfect, it remains, for me, one of the best animated shows to come out of Japan in years. Ideally, you should simply sit and watch the whole thing in all its inventive, funny and deliciously odd glory.