RPG's by far are my Favorite. I don't really have a preference over East or West, just as long as it's open map with a meaningful story to it. Games like Oblivion and Skyrim, I can play for ever.
I also love MMORPG, first one I played properly was age of conan. I actually vowed never to play one of these types of games, but I was in game (uk shop) and picked up AOC thinking it was a hack and slash game, was pissed of when I got home and found out it was a MMO. So I tried it anyway, since I bought it. June the 2nd 2008 was the day I started playing, and I didn't stop playing it until January 2011. So yeah, I was hooked.
FPS's are kind shit these in regards to single player campaigns, the only exception I can think of is Dead Space 3 and Borderlands 2 (which is excellent). FPS these days are designed with multiplayer in mind, the single player campaigns are an afterthought, which is a waste really. However Battlefield 2 & 3 have excellent multiplayer arena's. I love the BF2&3 multiplayer game with their destructible buildings and massive maps, also the way team play is encouraged as opposed to a game like COD where always seems to be everyman for himself (which is fine if thats how you prefer to play).
I love beat-em-up's as well. Street Fighter, Tekken, Mortal Kombat. I just wish somebody would make a really good first person hand to hand combat game, with FPS style maps... that would rock. I also love the WWE games, and would have loved to have played the UFC games, these are only type of games where I still wished I owned a console.
I loved the horror genre's as well... I say loved because I don't think I've seen a decent one since Doom 3. Dead Space is ok, but not really scary. Give me a game that has the tension and holy shit moments of Resi 2 and the eerie atmosphere of silent hill.
Finally I love me a good old sandbox game. GTA's are awesome, FarCry's are awesome, Saints Row's are awesome, Infamous 1 & 2 are both awesome. A lot of people haven't played Just Cause 2 yet, a little tip, if you haven't played this game it will surprise the shit out of you, it was probably my favourite game of 2010.
There is one Genre that I avoid at all costs - Platformers. I cannot stand these types of games.