If it's not obvious given the size of this post, I'm extremely interested in games and gaming. I try to keep up with the industry and at one point was sure I was going to work in said industry. Not entirely sure about that now, but I find it fascinating nonetheless.
Much easier to list the (types of) games I
don't like, really. That amounts to old '90s point-and-click-adventure games (not entirely sure why I could never get into them) and real time strategy games (I can do reflex-based play or thought-based play, but not both at the same time, heh).
I trend heavily towards RPGs, especially turn-based strategy ones (ala Final Fantasy Tactics, Disgaea, the Devil Survivor games), with 4x (think Civilization) games close behind. Then pretty much any generic 'action' (survival horror, third person shooter, first person shooter, adventure, whatever) and then everything else.
Giving honorable mention to Morrowind; It was the first huge open world game I ever played and my heavy involvement on the GameFAQs boards is what turned me into the Internet and computer buff I currently am. Arx Fatalis is another quirky first-person RPG that shares this honor.
Among commercial games, a few of my all-time favorites (here defined by number of times I've played through) are
Deus Ex (the original; haven't played Human Revolution and was under-impressed by Invisible War),
both of the Star Wars: KotOR games,
Silent Hill 2,
certain entries in the Legend of Zelda series (the original, LttP, OoT, MM),
the original Final Fantasy (I think I've played nearly every remake),
and Sword of the Stars (the original; my computer won't run SotS2 and that's a bit of a mess right now anyway). EDIT: Since someone mentioned Homeworld upthread, I figured I should mention that I think some of the same guys worked on this game.
Oh! And X-COM. The original one from 1993. Only discovered it recently and had no idea what I was missing. Excited for the coming-soon non-FPS reboot.
The first two Fallouts.
The Halo series (which is both overhyped and overhated).
Guild Wars and the two expansions that weren't awful (I am excluding Factions. Screw Factions so hard.)
I'm also big on non-commercial games. This includes a number of increasingly obscure roguelikes (Dungeon Crawl: Stone Soup, Cataclysm, whatever the heck ToME4 stands for now),
Dwarf Fortress, Aurora (which is more of a spreadsheet simulator than a game but enjoyable to me nonetheless), Iji, Gang Garrison 2, and no doubt a lot of other stuff I'm not thinking of.
Also some bigger commercial 'indie' games like Minecraft and Terraria.
I think I'd play a lot more online multiplayer, but I live rurally enough that I can choose between two god-awful connections that are only sufficient for really old or really simple games.