Game: Tie between R/S/E (I've played all three), Pearl, SoulSilver, and XD: Gale of Darkness.
Haven't played much of Generations I and II; I found Black to be a really good game but it was lacking in some departments; I think X is kind of a mess, but still a worthwhile experience. Also, my brother bought Alpha Sapphire, and he offered to let me play it, but I haven't gotten around to it yet.
Favorite game is probably Omega Ruby because Gen VI is nearly perfect and Genn III is nostalgic. My favorite pokemon is probably Furret because about 2 year ago my friend caught a shiny Furret in Soul Silver and she decided to name it after me. She then became my girlfriend. (She's way too luck though. She caught a shiny Houdoom in Pokemon X, and those are the only 2 Pokemon games she has played.)
My favorite pokemon game is Yellow and my favorite pokemon is Snorlax. One of my favorite teams I ever set up had two Snorlaxes. One was a physical attacker with body slam, earthquake, rock slide, and selfdestruct. The other was a special amnesia attacker (back when anemsia raised offensive special as well since special was still combined) with amnesia, ice beam, thunderbolt, and selfdestruct/fire blast (I forget which final move I stuck with). Between the two of them, they had most types covered.
Hmm... favorite one? That's an actually really tough question...... hmmmmm...
I think I have to go with Pokemon Red, and Fire Red because they made a lot of very good improvements.
Favorite Pokemon, two way tie between Charizard and Tyrantrum. Charizard has always been my main man, and I feel like they made Tyrantrum just for me.
Bonus answer: least favorite game/generation is Sapphire/gen 3. Utter garbage. Well I mean that's subjective obviously but I hated most of the pokemon in it and the gym leaders were an joke, and a poor one at that. There's no excuse to have one of the final gym leaders use only two pokemon (that suck). I went through the entire thing with only 5 pokemon, didn't find even a sixth one that I liked until I got to the elite four, and forced myself to go back and find something usable (Duskull ftw). A boring slog of a pokemon game and I'll never touch it or any iteration of it again.
EDIT: actually explaining why I didn't like gen 3 so I don't sound like I'm just trying to piss people off.