While I still play them, I've mostly gotten out of most FPS games these days (3 guesses as to why).
Another genre I've mostly dropped out of is 2D platforming, but mostly due to the lack of must have games (yes I did pick up Outland, and yes I enjoy it, but I've not seen a lot in this department as of late). This one is probably the one I'd come back to the quickest if I saw more of it.
Fighting games have basically dropped off my radar these days. Between the fact that I don't want to have to buy the newest version of a game (or get the huge DLC for it, and definitely not the small DLC costumes). The exception here is BlazBlue, which is helped by having a good story that I actually got invested into. However, my previous favorites such as Soul Calibur, Tekken, and even MvC went down or are currently going down a road I'm not following.
JRPGs surprisingly still remain as one of my more favored genres, though it's also the genre I see the most disappointment in (doesn't help that finding reviews by people who have actually played through enough of the game to give a good overall opinion are harder to find than most of the games themselves). I'm a bit tired of Strategy JRPGs (ie same system as FF Tactics) though, but that's more because you can't toss a stone in the PSP library without hitting 50 of those.
MMOs are a genre I keep falling back into. Never got addicted to WoW, but CoH (and way before that Runescape) was a nice timesink. Guild Wars was what I played with my friends back in High School, and these days I'm trying out Champions Online while looking over at TOR (and knowing that my crappy internet wouldn't be able to handle it even if I wanted to pay subscription). It always ends up with me taking long breaks between MMOs but I keep falling back into them.
If we were to names series that are practically their own genres at this point based on their fanbase size, I've fallen out of plenty (Halo, Megaman, Pokemon, Mario, etc.).