Too hard, so many choices.

Best Action/ Adventure Games
Uncharted 3
Metal Gear Solid 4
Red Dead Redemption

Best Fighting Games
Persona 4: Arena
Playstation All-Stars Battle Royale
Super Smash Bros Brawl

Best First Person Shooting Games
Call of Duty 4: Modern Warfare
Call of Duty: Modern Warfare 2
Battlefield 3

Best Platforming Games
Super Mario Galaxy
LittleBigPlanet

Best Sports Games
F1 20XX
FIFA XX

Best RPG Games
Tales of Vesperia
Final Fantasy XIII
Pokemon Heart Gold / Soul Silver
Crisis Core: Final Fantasy VII
The Elder Scrolls V: Skyrim

Best Third Person Shooters
The Last of Us

Overall Best Games
Final Fantasy XIII
Tales of Vesperia
Metal Gear Solid 4
Call of Duty 4: Modern Warfare
Assassin's Creed 2

Why? A great game is a great game no matter how big or small the hype on it is.

For me, SO FAR it's the Last of Us.

You may also want to play all of those games on your list. 

THe best games for me this generation are:

The Last of Us

Uncharted 2

Persona 4:golden

Ni No Kuni

Ratchet and Clank: A crack in time

The World Ends with you(can I include this?)

Tekken Tag Tournament 2

Kingdom Hearts Birth by sleep

and so on...too many actually. those are just the one i can remember

LOL at what you said for fighting games. 

SMG and Xenoblade.

Then a bunch of other real good games like Batman, Mass Effect...

Arkham City

Games that stuck out for me were God of War 3, GTA 4, Skyrim, TLOU, Super Mario Galaxy, and many others that I seem to have forgotten.

I don't think handheld games count... And Persona 4 Golden is a port of a PS2 game (a great game though) so is certainly cheating

Handheld games obviously count, the PSP and the NDS were also from this generation...
by the way...

Best handheld game: Daxter

To answer the poll, Super Mario Galaxy is pure gameplay masterpiece at it's finest, meanwhile The Last of Us is only storytelling/character development at it's finest. It pains me to see that today's so called gamers look at shallow things like story and voice acting to let them selves get hypnotised/brainwashed into thinking that a game is good or not. Gameplay>>>>Story and TLOU had nothing special whatsoever in the gameplay department.

Best Action/ Adventure Games: Legend of Zelda: Skyward Sword
Best Fighting Games: I don't play those much, Super Smash Bros Brawl was the only one I really liked. By far the most fun for me but I would'nt say it's the best cause it has it's share of flaws.
Best First Person Shooting Games: Bioshock
Best Platforming Games: Super Mario Galaxy2
Best RPG Games: Xenoblade Chronical
Best Third Person Shooters: Uncharted2
Overall Best Games: Really hard to choose cause all genres are so different. But like I said, Galaxy is pure gameplay and level design masterpiece, so I'd go with this game.