I'm not quite sure I can answer these questions with any sort of definitiveness. In my mind, picking a favorite game is like picking a favorite child or a favorite Short Pause partner; there are too many options that are equally as good as the next (I mean, it's easy to throw Felsing out of the mix, but it becomes more difficult when picking favorites between Eric and Taz). When I think about favorites, Metal Gear Solid immediately comes to mind, in particular, Metal Gear Solid 2: Sons of Liberty. I remember this being such a landmark game at the time. It had this crazy off-the-wall story with these insane, mind-of-Kojima-villains (Fatman!), and it was just so effin' fun to play! The graphics were unbelievable for its time, and the fact that you played as Raiden instead of Snake for the majority of the game was an honestly shocking story twist. The gameplay took the stealth mechanics of the original Metal Gear Solid and bumped it up to the next level, resulting in an engrossing experience that somehow managed to one-up the supremely awesome first series entry. While I still hold a special place inside for the first game's story and villains — quite possibly the best of the entire series — Metal Gear Solid 2 was a sequel that truly felt "next-gen" and it's definitely one of my favorite game experiences ever.
There are so many more games I can mention here. I remember playing Tony Hawk Pro Skater 3 with my roommates in college for what must have been hours everyday for three months straight. Then there are the long Super Smash Bros. Melee and Brawl sessions that would last into the wee hours of the morning. I spent 200 hours doing and finding everything in Final Fantasy VII, while Pokémon Diamond sapped almost 325 hours out of me when I became obsessed with breeding the ultimate Pokémon. Castlevania: Symphony of the Night is the reason I love "Metroidvania" games. Oh, and I can't forget Super Mario World, Mega Man 2, Resident Evil, Street Fighter (all of them!), Final Fantasy IV, Uncharted, Super Stardust HD, Pixeljunk Eden, and on and on and on and on...
So yeah, that's my long way of kind-of-answering the question.
And a special mention to The Last of Us. I'm not sure it's been out long enough to top the "Best of" list yet, but it's quickly making its way up the ranks as the standout game of the previous generation.
As far as games I can always go back and play, I think Street Fighter is probably the best answer for me. I can always boot up the latest entry in the series (Ultra Street Fighter IV in this case) and have fun going a few rounds. When playing with friends, I can go on playing match after match forever. I've loved fighting games since I was a wee lad, and I have Street Fighter II to thank for that. If I'm watching a match, or start talking about the game with someone else, the first thing I want to do afterwards is fire up the game myself and see if my Ryu can still hold his own.
There are probably an infinite number of games I could fire up as a time waster to kill a few minutes. Housemarque staples Super Stardust HD, Dead Nation, and Resogun are all great options. Hotline Miami is one I can always jump into at a moment's notice and try to get one more A+. My go-to time waster may very well be Spelunky, though. It stays forever installed on my Vita, and it's something I can always revisit to try and improve my time and ability. I've yet to make a successful Hell run, so this little feat remains on my gaming bucket list.