Well, I call myself a gamer yet I rarely actually beat games. I usually get bored before beating them.

Games I've Beaten

NES:
Super Mario Brothers

Nintendo 64:
Super Mario 64
Star Fox 64
GoldenEye 007
Perfect Dark
Mario Kart
NBA Hang Time
NBA Show Time

Nintendo Gamecube:
Mario Kart Doubledash

Sega Game Gear:
Sonic
Sonic 2

Sega Genesis:
Sonic the Hedgehog
Sonic the Hedgehog 2
Dr. Robotnik's Mean Bean Machine
Jurassic Park
NBA Jam

Sega Saturn:
NiGHTS: Into Dreams
Jurassic Park: The Lost World

Playstation 2:
Timesplitters 2

PC:
Sim Ant
Sim City
Pitfall: The Mayan Adventure

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Games I've Started

NES:
Super Mario Brothers 2
Super Mario Brothers 3
The Legend of Zelda
N.A.R.C.

Super Nintendo:
Super Mario World
Street Fighter 2
Donkey Kong Country
Donkey Kong Country 2

Nintendo 64
Turok: Dinosaur Hunter
Turok: Rage Wars
The Legend of Zelda: The Ocarina of Time
The Legend of Zelda: Majora's Mask
Jet Force Gemini
Donkey Kong 64

Nintendo Gamecube:
Super Mario Sunshine
The Legend of Zelda: Windwaker

Nintendo Wii:
Super Mario Galaxy
The Legend of Zelda: Twilight Princess

Sega Genesis:
Sonic the Hedgehog 3

Sega Dreamcast:
Crazy Taxi

Playstation:
Crash Bandicoot
Tomb Raider

Playstation 2:
Grand Theft Auto III
Baldur's Gate 2: Dark Alliance 2
Final Fantasy X

XBOX:
Halo
Halo 2
Rainbow Six 3
Splinter Cell
Splinter Cell: Pandora Tomorrow

PC:
StarCraft
WarCraft III
Half-Life
Half-Life 2
Ghost Recon
Splinter Cell: Chaos Theory

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So yeah. I don't finish many games. Those are all the games I've beaten or started (off the top of my head). By started I'm referring to games that I played a good ways into.

I'm sure there are a lot more that I've started that I just can't think of. I'll add any if I think of them later.

ill name what i can

Super mario bros(cant remember exactly which ones but theres quite a few)
all the gtas(3 and up)
every metal gear/solids
medal of honor allied assault
warcraft 3
call of duty 4
warriors
manhunt 1&2
every tony hawk game(except downhill jam)
donkey kong country 1-3
assassins creed
guitar hero 3
halo 3
starfox 64
diddy kongs racing

thats all i can think of right now

Ok here goes:
Super Mario 64
The legend of Zelda
Super Mario Bros.
Super Mario Bros. 2
Super Mario Bros. 3
Super Mario Bros. The lost levels
Super Mario World
Super Contra
The legend of Zelda: a link to the past
The legend of Zelda Ocarina of time
Metal Gear Solid
Metal Gear Solid 2
Red Faction 2
Half Life
Half Life 2 + Episode 1&2
Portal
F.E.A.R
Project Gotham Racing 2 (Including ALL Platinum Medals)
Project Gotham Racing 3
Gran Turismo
Gran Turismo 2
Gran Turismo 3
Splinter Cell
Grand Theft Auto 3
Grand Theft Auto Vice City
Medal of Honor Frontline
Medal Allied Assault
Medal of honor Rising Sun
Call of Duty 2
Call of Duty 4
THPS
THPS3
Deus Ex: Invisible War
Donkey Country 2
Halo
Halo 2
Super Mario Kart 64
Resident Evil 2
Resident Evil 3
Formula One
Formula One '97
Goldeneye 007
Timesplitters 2
Street Fighter 2 (most incarnations)
Killer Instinct
New Super Mario Bros.
Double Dragon 2
Toca 2
Race Driver
Race Driver 2
Race Driver 3
Air Combat
Ace Combat 3: Electrosphere
Super Mario Kart DS
Doom
Doom II
Doom 3
A Boy and his Blob
Assault Rigs
Battle Arena Toshinden 2
Tekken 2
Tekken 4
Destruction Derby 2
Mortal Kombat
Mortal Kombat 2
Need for speed
Porsche challenge
Sonic the hedgehog
Sonic the hedgehog 2
Alex the kid
Road Fighter
Sword Master
007: Agent under fire
007: Nightfire
Earthworm Jim
Terminator 2
T2: The arcade game
Rainbow Six: Black Arrow
Grand theft auto: Liberty City stories
Zombies ate my neighbours
Hercules
Final fantasy VIII
Renegade
Thats about all i can remember at the moment

I'm not exactly sure I'll get all of them but here goes.

Zelda Games
1. The Legend of Zelda
2. Ocarina of Time
3. Wind Waker
4. A Link to the Past

Mario Games
1. Super Mario World
2. Mario 64
3. Mario Kart 64
4. Mario Kart Double Dash
5. Mario Kart GBA
6. Super Smash Brothers

Blizzard Games
1. StarCraft
2. StarCraft: Brood War
3. WarCraft III: Rein of Chaos
4. WarCraft III: The Frozen Throne

Half-Life Games
1. Half-Life
2. Half-Life: Blue Shift
3. Half-Life: Opposing Force
4. Half-Life 2
5. Half-Life 2: Lost Coast
6. Half-Life 2: Episode 1
7. Half-Life 2: Episode 2
8. Half Life Source

Star Wars Games
1. Star Wars: The Phantom Menace
2. Star Wars Podracer (for N64)
3. Jedi Knight II
4. Star Wars Galactic Battle Grounds
5. Star Wars Episode II (for GBA)

Other Games
1. Perfect Dark (Perfect Agent)
2. Goldeneye (Secret Agent)
3. Dungeon Siege
4. Dungeon Siege: Legends of Arana
5. Total Annihilation
6. Halo (Legendary)
7. Age of Empires
8. Toy Story (PC)
9. Legacy of Goku
10. Legacy of Goku II
11. Sonic The Hedgehog
12. Sonic The Hedgehog II
13. Sonic (the one for GameGear)
14. StarFox 64
15. Hook (for GameGear)
16. Balder's Gate 2: Dark Alliance
17. Time Splitters
18. Dr. Robotinik's Bean Machine
19. Jurrassic Park: The Lost World (Sega Saturn)
20. Knights (Sega Saturn I think)
21. Lord of The Rings: The Two Towers
22. Lord of The Rings: The Return of the King

Games that can't be beaten but I've played
1. Animal Crossing
2. Counter-Strike: Source
3. Day of Defeat
4. Day of Defeat: Source
5. Half-Life: Deathmatch
6. Half-Life 2: Deathmatch
7. Team Fortress
8. Team Fortress 2
9. BattleField 2
10. BattleField 2142: Northern Strike
11. Half Life Source: Deathmatch
12. Ricochet

oh man I totally forgot about my good old game gear.

Game Gear
Sonic The Hedgehog
Sonic The Hedgehog 2
Sonic Chaos
Hook

PC
Sim City
Sim Ant
Dungeon Siege Legends Of Aranna (if saying the original dungeon siege doesn't count I've beaten the first one and the expansion which is LOA)

Playstation
Crash Bandicoot Warped
------
it really helps to see games that other people put down and then remember that you have beaten that game too.

Uh oh, here comes the equivalent to a shrink ray for my e-****.

WC3, Halo1, Halo2

Only games ive owned.

Golden Sun
Golden Sun: The Lost Age
Fire Emblem
Fire Emblem: The Sacred Stones
Donkey Kong Country
Castlevania: Circle of the Moon
Kingdom Hearts 2
Need For Speed Most wanted
Need For Speed Carbon
Sphinx and the Cursed Mummy
Starfox Adventures
and more I can't remember at this current time.....

Games I have beaten:
Super Mario Brothers
Super Mario Brothers 2
Super Mario Brothers 3
Super Mario Brothers All Star
Megaman
Megaman X
Megaman Zero
Megaman Zero 2
MegaMan Zero 3
MegaMan Zero 4
Megaman ZX
MegaMan Battle Network
MegaMan Battle Network 2
MegaMan Battle Network 3 Blue
MegaMan Battle Network 4 Red Sun
MegaMan Battle Network 4 Blue Moon
MegaMan Battle Network 5 Team Protoman
Yugioh Dark Duel Stories
Pokemon Red
Pokemon Blue
Pokemon Gold
Pokemon Silver
Pokemon Yellow
Pokemon Crystal
Pokemon Ruby
Pokemon sapphire
Pokemon Diamond
Pokemon Pearl
Golden Sun
Golden Sun 2
Yugioh Reshef of darkness
Yugioh World Championship '08
.hack//infection
.hack//Mutation
.hack// Outbreak
.hack//Quarantine
.hack// GU Rebirth
.hack// GU Reminisce
.hack// GU Redemption
Kingdom Hearts
Kingdom Hearts II
Street Fighter for the GBA
Super Smash Brothers Melee
Luigi's Mansion
Sonic Adventure 2 Battle
Pokemon Colosseum
Tony Hawk 3
Viewtiful Joe
DBZ Budokai 2
DBZ Budokai Tenkaichi 2
DBZ Budokai 3
DBZ Budokai


THere are prolly more that I cannot think of at the moment

Halo
Halo 2
Halo 3
Half-life
Half-Life 2
Half-Life 2 Ep.1 & 2
Half-Life blueshift
G.R.A.W.
S.T.A.L.K.E.R.
Abe
Castlevania SOTN
Legend of Zelda: Wind Waker
Metal Gear Solid
Metal Gear Solid 2
Metal Gear Solid 3
Portal
Time splitters
Time splitters 2
Time splitters 3
Elder scrolls IV: Oblivion
Battle field 1942
Splinter Cell: pandora tommorow
Splinter Cell: chaos theory
Splinter Cell: Double agent
Psychonauts
Medieval Total War 2
Shogun Total War
Rome Total War
Tony Hawk's proskater 2,3,& 4
Company of heroes
Battle for Middle Earth
Battle for Middle Earth 2
Assassin's Creed
Call of Duty
Call of Duty 2
Call of Duty 4
Guitar Hero
Guitar Hero 2
Guitar Hero 3
Balder's Gate
Balder's Gate 2: Dark alliance

Booooooo~ The only Baldur's Gate 2 anyone should be playing is Shadows of Amn