wow, big question.
i have a tough time answering this one because i've played so many great games, a few of them even here on AG. however some of my favourite games are need for madness(crazy raceing game, try it out its free), Okami(holds the world record for least sales for a best game of the year award winner at around 200,000 copies sold in 2010. it was originally released for ps2 right as the ps3 came out, and then was later converted to wii), rachet and clank: a crack in time(i just got this recently and its too short), X-Wing vs TIE fighter(an old lesser known star wars dogfighter, (im a 1st class republic general), with decent graphics and amazing gameplay), andthe portal series, of course, i never get tired of POtatOS.
i dont think ive listed everything here, but i did my best

My favourite game would definitely by Skyrim. It has many things to keep you busy like quests, errands ad so on. Also, people don't respawn (I find this a good thing) however some NPC's are un-killable until you complete the quest that they are involved in, rendering the NPC killable. So, once you complete ll the quests... YOU CAN KILL THE WORLD! MWAHAHAHAHAHAHA! Or you can leave it.... nah, too boring :)

I would say that the my favorite games are

Sonic Adventure (DX Director's Cut)
Sonic Adventure 2 (Battle)
Golden Sun
Chrono Trigger

Sonic Adventure and its sequel (Sonic Adventure 2) are two of my favorite games because of the music. I also like raising the Chao. (For those who don't know, Chao are little alien-things that you can raise. Virtual pets, one may say.)

Golden Sun is one of my favorite games due to, once again, the music. I also like the animations/special effects of the Psynergy, summons, and unleashes of (some) weapons. I also like the story/stories of the series.
(I remember a time when my cousin nuked the Earth with a summon.)

Chrono Trigger is a favorite of mine due to (once again. derp) the music. It's also because of how the combat system works. Instead of being turn-based like traditional RPGs, battles are always moving (real-time). I also like the story of the game. Time travel is cool.

I know Skyrim is a great game, i finished it 4 times, i mean the mais story and the factions, but I lovoed Kingdom Hearts, but in the future I hope it changes because it means that the game studios are making great games, what is good for most of us

marvel vs capcom 2

PSP - God of war
Ps3 - need for speed the run
Xbox - Halo
Pc - Skyrim

My top 10 Nintendo 64 listing:

I have played basically every title on the Nintendo 64, these 10 games are worth any kind of money:

1- Banjo-Kazzoie (The greatest designed game on the N64)
2- Paper Mario (It's insane awesome in every way except difficulty)
3- Ocarina of Time (It represents the zelda series, deff a top 3 pick)
4- Banjo-Tooie (Banjo Kazzoie on crack, nearly a better sequel)
5- Mario Kart (Defined being social with friends)
6- Super Mario 64 (A Great game, defined the 3D platformer)
7- Majoras Mask (Amazing despite it being a bit short)
8- Mario Party 2 (The greatest MP for a ton of reasons)
9- Diddy Kong Racing (I had fun with this game, despite the hate)
10- Super Smash Bros (It's a blast until your the only one playing)

It's almost an unfair question.  I'd say that I have different favorite for different console generations. 

For handhelds, my favorite game was Pokemon Diamond.  Yes, I enjoyed Red and Silver, but Diamond had great game mechanics.  And things weren't super crazy complicated yet.

For anything pre N64, I'd say Super Mario World for the Super Nintendo.  I played that so much I know all secret stages and most secret blocks.

For the N64 my favorite is probably Pokemon Stadium 1&2 for the mini games.  It was my favorite multiplayer format for the console.

Around Gamecube, PS2, original XBOX I got into KOTOR.  I still play it on my PC.

And for the modern systems, my favorite has to be Zelda Skyward Sword.  I appreciate the quality and playing hours of the game.  It's probably my favorite Zelda game.

I mainly play Wii, so here are my Top 5 Wii Games:

5. Super Smash Bros. Brawl
4. Call Of Duty: Modern Warfare 3
3. PokePark 2: Wonders Beyond
2. Call of Duty: Black Ops
1. Mario Kart Wii

Call of Duty Modern Warfare 3:
I like it because of survival mode.