For me, my favorite (other than Mario) has to be Disgaea (if you count the new PSP title as part of the series; just got a preview build last week and I LOVE it) or Metal Gear Solid. Had Encore: Rocks the 80s not been such a disappointing game, Guitar Hero would be up there. I haven't really loved what I've been playing of GH3, though, so it looks like it's downhill for the franchise after Harmonix left
I'm older and I used to love the games like Nobunaga's Ambition and others like it (even ones like Aerobiz). Back in the early days, I loved C&C. Alas, I'm out of my teens and twenties and video games just don't factor in much. I play Guitar Hero I and II more than anything. And since I had one of the first Nintendo NES systems out, Mario will always have a place in my heart.
For new style of games, I love grand theft auto franchise. But I always love to play mario and sonic since I was young.
Twinbee without a doubt. My favourite game of all time is Pop'n Twinbee for SNES, I still play it about once a week (on my GP2X). In this century it's the Gran Turismo series.
I love the original mario games and super smash brothers, but my all time favorites are the harvest moon games
Grand Theft Auto. It seems like each new game in that franchise gives the character more and more freedom to do whatever he wants and go anywhere.