I used to play 70+ hours a week of games, now I play much less, but I still play often enough. I like videogame RPGs (role-playing games) like, I have no experience with table-top (D&D for example), some puzzle games, some shmup* games and maybe a few racing games. Some platform games. I abhor first-person shooting games.
*shmup = shoot them up -and that's not a first-person shooter, that's those old-school games where you're a small spaceship in the sky/space and you shoot enemies all over the screen while avoiding being killed. Examples include Gradius, 1942, Starsoldier, Starforce, Section Z, TwinBee, Shikigami castle and DoDon Pashi Daioujou.
Puzzle games I like include mainly Bust-a-Move series games with Bub and Bob, they're more exciting than Tetris anyway. And old game of the genre, besides Tetris, would be Flipull, or Puzznic.
Platform games include Super Mario series, MegaMan series, Adventure Island series, Ninja Gaiden (old series) and such. I usually stick within a series and don't like them all...though platform were probably some of the most widespread 2d side-scrolling genre.
I tried a few FPS, and couldn't even stand to play 10 minutes. The only one I even liked is Final Fantasy VII: Dirge of Cerberus - and that's because I'm an unconditional Final Fantasy fan

I had to beat it. My brother is about 10x better than me.