This is actually a pretty neat idea. I dug up a list I made in 2003 that has my favorite games for each year from 1991 to 2002 (I only considered the years for which I played most of the notable games) and some mini-reviews for the games, from which I included a synopsis for each game. I made it by looking through old magazines back then but haven't updated it since.
1991:
Super Mario World - This was the first Mario game I made serious progress in. I loved my time with this game, trying to figure how to get all the secret paths.
Runner-up:
Nothing else during this was worth considering...
1992:
Legend of Zelda: A Link to the Past - The best Zelda game ever. Thanks to the map and in game hints, I never felt frustrated with this game. I loved exploring it.
Runner-ups:
Super Mario Land 2 - I loved this game though it's considered crap by Mario standards.
Super Mario Kart - This was my first multiplayer game. This game kicked ass on all sorts of levels... still can't decide if this or Mario Kart 64 is my favorite Nintendo MP game.
1993:
Legend of Zelda: Link's Awakening - This was my first Zelda game and it took me years before I actually beat it (no FAQs back in those days).
Runner-up:
Secret of Mana - The scenery and music in this game was beautiful. The gameplay was awesome if you could get someone to play with you... otherwise it was nowhere nearly as fun.
1994:
Final Fantasy III - Still the best FF game ever. The epitome of traditional ATB, characters that actually showed gradual and emotional evolution, a villain you loved to hate and an ending that left you satisfied.
Runner-up:
Super Metroid - The atmosphere of this game blew my young mind... I never did beat it though.
1995:
Chrono Trigger - The best RPG and best game ever made, IMO. An awesome battle system, fantastic story, multiple ending (even one where the world ends!), New Game +, and still the best music in a video game combined to create something that will likely never be imitated again.
Runner-up:
Super Mario World 2: Yoshi's Island - Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! Wah! ...Doesn't matter, still awesome.
1996:
Super Mario RPG - A game that combines Nintendo + Square at their primes? Hell yeah! I loved the style, the humor, and light hearted nature of this classic.
Runner-up:
Super Mario 64 - To this day, I'll never forget the feeling of experiencing freedom (especially when flying) first time. It was the first game I fully completed.
1997:
Final Fantasy VII - I remember having a lot of trouble with this year... so many awesome games but I think FFVII wins out. It's the game that started my love affair for RPGs with its story, music, characters and battle system (the material system is still the best in regards to customization).
Runner-up:
Goldeneye 007 - So many hours spent on the MP... so many hours...
Castlevania: Symphony of the Night - I never liked Castlevania games since I found them difficult but this game was enjoyable and the fused RPG elements definitely helped. But enough talk, have at you!
More runner ups: Star Fox 64, Mario Kart 64, Wild Arms, and Blast Corps.
1998:
Legend of Zelda: Ocarina of Time - 98 had an insane amount of awesome games and was way more difficult to choose than 97, but OoT wins out simply because it was A Link to the Past in 3D and the Z-trigger lock-on was such an innovative idea.
Almost GotY:
Xenogears - One of my favorite RPGs and games, thanks to an awesome combat system, engrossing story and probably one of of best OSTs. It's only downfall is the second half, which I actually enjoyed but was clearly rushed and could have been so much more... wish we got to see the ohter arcs of this series.
Runner-ups:
Half Life - The combination of story, puzzles and the FPS genre made this game unlike any other before.
Metal Gear Solid - It took some patience but the cinematic feel of this game and stealth based gameplay was cool. I also think it's the first game to make you look at the back of your game case and the first to read what's on your memory card...:lol:
Final Fantasy Tactics - Never was good at SRPGs but I definitely spent time behind this game. Love the story of intrigue and backstabbing and the near perfect gameplay.
Pokemon Red/Blue - For some reason, as much as I loved this game, I never cared as much for any of the sequels because they all lacked the simple charm this game had. Most of the sequels just added more (uninteresting) Pokemon.
1999:
SoulCalibur - I remember getting my DC and this game days after it came out. I never liked fighting games but this game was just so easy to get into and fun to play.
Runner-up:
Gran Turismo 2 - God I hated those license tests... because as soon as those were done, I'd save up money for a 3000GT, suped it up to 933HP and kill everyone.
Super Smash Bros - What needs to be said here? This game was just fun, pure and simple.
2000:
Chrono Cross - Being the sipritiual successor to CT, of course I was hyped for this game and it did not disappoint. The beautiful graphics and music (Time's Scar was just... my god!), the fantastic battle system, the engrossing (if a bit confusing) story lived up to my expectations... the only downside was the 40 character, of which, ~5 had actual personalities/back-stories.
Runner-up:
Vagrant Story - I love the whole espionage/RPG element to this game and the battle system was insanely deep. I spent hours grinding/level weapons.
2001:
ICO - I ignored this game for a long time but when I finally got it, it completely changed my perception of video games. It's such a beautiful game on so many levels...
Runner-up:
Grand Theft Auto III - Like Mario 64, this game also provided a sense of freedom unlike any before it. It was so much fun playing the game and having the option to do so many things.
2002:
Metroid Prime - Like Super Metroid, the atmosphere in this game was so engrossing and captivating. While others complained of the controls, I loved them. Motion controls ruined the adventure feel of this series and turned it into a crappy FPS.
Runner-up:
Eternal Darkness - Oh man, the sanity effects in this game were so cool. I thoroughly enjoyed the very dark and gritty story and setting for this game, and loved how it used the different charaters to provide very unique gameplay styles.
That's the last year I have it updated for. Don't have the mini-reviews from here on out, so just the names and box art.
2003:
Legend of Zelda: Wind Waker
Runner-up:
Panzer Dragoon Orta
2004:
Half-Life 2
Runner-up:
Metal Gear Solid 3
2005:
Resident Evil 4 (GameCube)
Runner-up:
God of War
2006:
Okami
Runner-up:
Gears of War
2007:
BioShock
Runner-ups:
Call of Duty: Modern Warfare
Super Mario Galaxy
Mass Effect
God of War II
2008:
Fallout 3
Runner-up:
Metal Gear Solid 4
2009:
Uncharted 2
Runner-up:
Batman: Arkham Asylum
2010:
Red Dead Redemption
Runner-up:
God of War III
Mass Effect 2
2011:
Legend of Zelda: Skyward Sword
Runners-up:
Skyrim
Radiant Historia 
