PC:
StarCraft Battle Chest
Diablo II
The Orange Box*
SPORE
Hellgate: London (good thing I couldn't do online play anyway, eh?)
BioShock Limited Edition
Quake III Arena
Starsiege: Tribes*
Magic Carpet Plus
Duke Nukem 3D CD (includes Duke Nukem and Duke Nukem 2)
Lords of the Realm II
LEGO Star Wars
MapleStory*
Robot Arena
Pac-Man: Adventures in Time
Some stupid generic sudoku thing
Psychonauts
Civilization III*
3D Ultra Pinball: Thrillride
Tetris Worlds
Forgotten Realms Classics (a collection of a bunch of Forgotten Realms DOS games; IMO, the only good things in it are Dungeon Hack and Blood & Magic)
Some sort of paintball game
Icewind Dale II
Pong
Missile Command
Combat
Midway Arcade Treasures
Konami Collector's Series: Castlevania & Contra
Test Drive
Need For Speed: Hot Pursuit 2
Monty Python's The Meaning of Life
Abra Academy: Returning Cast
Glyph
World of Goo
Trials 2 Second Edition
Civilization III Complete
Civilization IV Complete
X-COM series
Audiosurf
Counter-Strike + Condition Zero
Eets
Eternity's Child (still blame Sunbun!)
Half-Life
Opposing Force
Blue Shift
Team Fortress Classic
Half-Life 2: Deathmatch
HeXen
HeXen: Deathkings of the Dark Citadel
HeXen II
Heretic: Shadow of the Serpent Riders
I-Fluid
Prey
RIP Trilogy
Blake Stone: Aliens of Gold
Blake Stone: Planet Strike
Games marked with an asterisk are marked as such because even though I own them through Steam (the Orange Box, Civilization III due to Civ3 Complete) or they're free downloads (Tribes, MapleStory), I own disc versions. I'm not counting games I have but don't own (meaning stuff like Jagged Alliance 2 or the WarCraft III Battle Chest, which I borrowed from my uncle - though I do own the soundtrack for the latter) or free games I don't own on disc (such as Red Alert or StepMania).
DS:
Scurge: Hive
Puyo Pop Fever
Meteos
Tetris DS
Elite Beat Agents
Clubhouse Games (This is a tricky situation. I bought the game for Kalee, but then her younger brother broke her DS. Until she finds his, the DS is sitting on my desk, with the game in it. I don't play it, but I'm counting it in my games for whatever reason.)
I used to own Pokémon Diamond, but that's a bad story I don't want to go into again.
GB/C:
Tetris
Tetris Blast
Tetris Plus
Super Mario Bros. Deluxe
R-TYPE DX
Qix
Elevator Action
Burgertime Deluxe
Not listing any I can't remember.
GBA:
Wing Commander: Prophecy
Phalanx (port of the SNES version, minus the cool boxart)
Bomberman Tournament
Classic NES Series: Bomberman
The Lord of the Rings: The Return of the King (it's almost exactly like Diablo!)
Pinobee: Wings of Adventure
Tactics Ogre: The Knight of Lodis
Kingdom Hearts: Chain of Memories
Metroid Zero Mission
NAMCOMUSEUM (my dad also has a copy of this, and there's a third copy somewhere in this house)
Pac-Man Collection (actually my dad's, but it spends most of its time in my game collection)
Astro Boy: Omega Factor
Pokémon LeafGreen
I used to own approximately three times as many GBA games. I also have an e-Reader and several NES games, plus like five of the Air Hockey cards.
NES (note: this is mostly from memory, since my games are for the most part scattered around in my room):
StarTropics
Metal Gear
Super Mario Bros./Duck Hunt
Rock-n-Ball
Blades of Steel
Tetris (three copies)
Super Mario Bros. 3 (three copies)
Heavy Barrel
Xenophobe
Adventure Island
Dr. Mario
Spy Hunter
Donkey Kong Classics
Golf
Gauntlet
Klax
The Legend of Zelda
Wheel of Fortune
Burgertime
Lee Trevino's Fighting Golf
I own three consoles: two front-loaders and a top-loader (fun fact: Boo_penguin once offered me a front-loader as a trade for said top-loader).
Genesis:
Street Fighter II': Special Championship Edition
Mortal Kombat
Greendog: The Beached Surfer Dude!
Batman Forever
Maximum Carnage
The Jungle Book
Streets of Rage 2
Shinobi III: Return of the Ninja Master
Vectorman
Double Dragon V (blech!)
Sonic the Hedgehog 2 (two copies)
Pac-Man 2: The New Adventures (not quite as blech! as DDV, but still pretty bad)
Golden Axe
Sonic Spinball (still in package, something unique amongst my cartridge-based games, though I do have a few Genesis game manuals)
I also have a 32X and one game, Shadow Squadron.
I wish I had Columns.
PlayStation/PS2:
Chrono Trigger
Mega Man Legends
Risk
Centipede
Tony Hawk's Pro Skater 3
Pipe Dreams 3D
A Collection of Activision Classic Games for the Atari 2600 (I am not joking. This is the name of the disc.)
Gauntlet Legends
Lemmings 3D
WarGames: Defcon 1
Spin Jam
Digimon World
Qix Neo (actually just Volfied)
Pac-Man World
NAMCOMUSEUM Volume One
LEGO Star Wars
LEGO Star Wars II: The Original Trilogy
Guitar Hero
Guitar Hero II
Guitar Hero Encore: Rocks the '80s
Dance Dance Revolution SuperNOVA
Soulcalibur II
R-TYPE Final
Intellivision Lives!
Fantavision
Dragon Ball Z: Budokai
EyeToy Play
Kingdom Hearts II
Katamari Damacy
For some reason my sister's Harvest Moon: A Wonderful Life Special Edition disc is still in my case. I also have three unopened games sitting here (Brunswick Pro Bowling, Pinball Hall of Fame: The Williams Collection, and Cocoto Fishing Master) and some sort of board game collection I've never played.
GameCube:
Super Smash Bros. Melee
Viewtiful Joe
Super Mario Sunshine
The Lord of the Rings: The Two Towers
The Lord of the Rings: The Return of the King
Tetris Worlds (the only reason I own the PC version at this point is because it includes the excellent soundtrack, which is shared between the PC and console versions)
NAMCOMUSEUM
Marvel Nemesis: Rise of the Imperfects
Spider-Man
Metroid Prime
Metroid Prime 2: Echoes
Crazy Taxi (my youngest brother also has a copy of this)
I also have a Game Boy Player, as does my dad.
We have an SNES, but it's my mom's and we only have one game (Wario's Woods) and at least one Super Game Boy (I don't know if my dad sold the second one or not). No N64. I have an Xbox, but it's another tricky situation. When we got it, there was a disc stuck between the drive and the case...and I don't have a power cord for it. Basically, I don't know what game I have for it or if it even works.
EDIT: Forgot a GBA game and decided to go back and add the GB/C games I could remember.
EDIT AGAIN: I actually have three copies of NES Tetris and SMB3. Whoops! Also added Genesis stuff which I completely forgot twice.
EDIT FOR THE THIRD TIME: Apparently I was thinking of something else entirely when I was doing PC games, and put the wrong name. It's Starsiege: Tribes, not Starscape.
