Genre
Mystery, Suspense, Noir
Mystery
Leonard might not be Sherlock Holmes, but he is, as Teddy says, "running around, playing detective." Teddy uses the word "playing," of course, because it's just a game to him. The real John G. is dead and Leonard's investigation is one of Teddy's (and possibly Leonard's) invention. But to Leonard the case is very real; it's his whole life. When he thinks he's finally solved the mystery by killing Jimmy, he realizes that the real culprit is Teddy and then purposefully lies to himself, giving himself another mystery to solve.
But this isn't just a mystery for Leonard; it's a mystery for the viewers too. There's a reason why the posters for Memento had puzzle pieces strewn about. Because of the close relationship between Leonard's perspective and our own, we're essentially trying to figure out the same mystery he's presented with… or is he creating it?
Suspense
Now wait just a minute. How can a movie be suspenseful when we not only know how it ends as a whole, but also know how each individual (color) scene ends because we've already seen how the previous scene begins?
Well, suspense isn't about not knowing; it's actually about anticipating the known. A situation is presented that readers or viewers know of and the suspense lies in the anticipation, anxiety, and dramatic irony that this future knowledge gives. So yes, we know that Leonard kills Teddy, but the suspense comes in finding out why.
Noir
Memento might not be shot entirely in moody black and white, but it actually fits the neo-noir genre to a T. If you check out our Best of the Web noir article, it says that:
Classic film noir conveyed a sense of dark pessimism, fear, mistrust and general insecurity that was rampant at that time. The use of black and white lighting, a morally ambiguous protagonist, a corrupt authority figure and a femme fatale were common among film noir plots. The endings were rarely optimistic.
Mistrust and pessimism? That's Leonard in a nutshell. He believes his only reason to live is to kill a man, and his notes are constantly warning to trust only himself.
Black and white lighting? Check… or make that half a check. Still, the past-tense scenes are indisputably B&W.
Morally ambiguous protagonist? Leonard is a man bent on revenge, tracking down a human being with the sole purpose on ending his life. But at the same time we understand his sense of justice and pity his constant disorientation.
Corrupt authority figure? Uhh, that would be a big yes. Teddy, you scumbag.
A femme fatale? Natalie is the poor beaten girl that Leonard must help only to find out she's the cause of a lot of his problems.
The ending? Well, it's not strictly pessimistic but it certainly isn't very happy… or very conclusive.