I'd say The Sims 3 is hands down my favorite. I'm also a big fan of Tetris and the Pokemon franchise. Most other games that I'm really into I've only watched people play, like Portal and Bioshock. I'm also pretty into the Phantasy Star games.
TES 3: Morrowind Star Wars Knights of the Old Republic (1 and 2 for different reasons) Mount & Blade Warband Kerbal Space Program << not to be underestimated ArmA series GTA San Andreas Honorable mention: Mirror's Edge, Portal, Splinter Cell: Chaos Theory I am loathe to choose one "best game ever" but all of these are stellar contenders for the title.
Fallout new vegas had just about everything i wanted in a game. And mirrors edge is still amazing to me no matter how many times i replay it. I just hope the new one doesn't mess it up.
I don't think it's my favourite game but the original Deus Ex is probably the best game I've ever played. A brilliant mixture of FPS, action, stealth and RPG. Excellent storytelling, great atmospheric music. Numerous ways to complete each level depending on your style of play: sneaking through vents, picking locks, hacking computers/robots, talking to NPCs, full frontal assault, etc.. So you never really feel penalised for the character development choices you've made (unlike Deus Ex Human Evolution!). It ticks a lot of boxes without ever feeling like it's spreading itself too thin.
Yoshi's Island on GBA Advance Wars 2 Kingdom Hearts I and II Pokemon Spelunky (It's an indie game, I really recomend it for those who want a challenge) Okami I think those are my favorites, can't remember if there is one missing.
Mine is probably one of four: Xenoblade Chronicles, The Legend of Zelda: Majora's Mask, Tales of the Abyss or Final Fantasy IX.
If I had to pick a single game, I'd have to go with either Disgaea or Braid. Both are the best at what they do. Disgaea has ridiculously fun gameplay, actually funny humor, and interesting characters. Braid is the most well-designed game I've seen with an absolutely beautiful integration of gameplay, narrative, and atmosphere. I have other personal favorites, but most of them are more "hit my gameplay/narrative buttons"-type games rather than games that are good in and of themselves.
