I'm a big fan of older games, my favorite game is most definitely Star Fox 64 (can anybody beat 1812 kills?). Right now I'm replaying a lot of my favorite games from childhood. On the 64, at the moment I am playing Majora's Mask for the first time and replaying Donkey Kong 64 for 100%.
On the gamecube I'm replaying Sonic Adventure Battle 2 for 100%.
On the ps2 I am finishing up Final Fantasy X and am halfway through FF7. I haven't played these before but I'm really enjoying them and am looking into older RPGs for the PSone. I've started Grandia, and Xenogears is next on my list.
However, at the moment I am in possession of an xbox 360 (and nothing else) so I gave into the temptation to try Skyrim. The only other xbox game at the moment I really like playing is Madden. I'm not a big fan of the FPS. The only shooters I really like are Battlefront and Metroid Prime.
I also do competitive Pokemon battling. If you're familiar with the online communities that do it, I think that those communities have ruined the game by banning way too much stuff. My friends and I came up with our own slimmer ruleset; it's just way more fun. Banning a bunch of stuff just takes the variety out of the game. If you play I'd love to battle you.