Well, this one is a no-brainer. Eternal Sunshine is a movie about two people falling love… and then out of love… and then in love again—except sort of in the reverse order… which is still the same order? Anyway, you get the picture. It's a movie that's driven by a romantic relationship, so it's first and foremost a romance.
Where the movie deviates from the romance genre is in its ambiguous ending. There's no final make-up scene when you just know everything is going to work out, all the problems will be solved, and everyone will live like Disney royalty. But there's also not a sense that are characters have really learned everything either, though they've probably learned that memory erasure isn't going to actually erase their problems, and that's something.
Eternal Sunshine is far from your traditional sci-fi flick, but unless you've seen some Lacuna ads around lately, the whole memory erasure procedure is definitely in the realm of science fiction. This element is what makes the film such a unique experience. What would it be like if Joel and Clem both suffered damage and simply couldn't remember each other anymore? It just wouldn't be the same, because the movie is less about the results of the procedure and more about the procedure itself and Joel's experience of it. The film is about Joel's literal journey through his own mind, something that would be impossible without a hint of the surreal.
Eternal Sunshine is a mystery in the sense that the viewer is forced to discover for him- or herself what is happening as the movie progresses. We're initially tricked: the film begins when Clem and Joel meet, and then it shifts to their break-up. We assume the film has jumped forward in time when really it has jumped backwards. We're left to uncover for ourselves what really happened, since everything we experience comes from Joel, not Clem. On top of that, Joel's memories unfold in reverse chronological order.
Part of Eternal Sunshine's draw is the puzzle of information we are provided. It's the mystery aspect of the film that really makes multiple viewings rewarding.