I'm just really bored, so I'm going to do this. Starting off with NES games.
In alphabetical order:

10-Yard Fight
1942
1943: The Battle of Midway
1999: Hore, Mitakotoka! Seikimatsu
3-D WorldRunner
4 Nin uchi Mahjong
720 Degrees
8 Eyes
'89 Dennou Kyuusei Uranai
A-Train
Aa Yaky%u016B Jinsei Icchokusen
Abadox
Action 52
The Addams Family
Advanced Dungeons & Dragons: Heroes of the Lance
Adventure Island
Adventure Island II
Adventure Island III
Adventures of Lolo 2
Adventures of Lolo 3
Adventures in the Magic Kingdom
The Adventures of Bayou Billy
Adventures of Dino Riki
The Adventures of Gilligan's Island
Adventures of Lolo
The Adventures of Rad Gravity
The Adventures of Rocky and Bullwinkle and Friends
The Adventures of Tom Sawyer
After Burner
Ai Sensei no Oshiete: Watashi no Hoshi (never got to play it though)
Air Fortress
Airwolf
Akira
Akuma-kun: Makai no Wana
Al Unser Jr.'s Turbo Racing
Alfred Chicken
Alien Syndrome
All-Pro Basketball
Alpha Mission
Altered Beast
Amagon
America Daitouryou Senkyo
American Gladiators
Antarctic Adventure
Anticipation
Arabian
Arch Rivals
Argus
Arkanoid
Arkista's Ring
Armadillo
Asmik-kun Land
Asterix (I don't remember playing this either)
The Astyanax
Athena
Atlantis no Nazo
Attack of the Killer Tomatoes
Aussie Rules Footy
Baby Boomer (better to own it then play it)
Back to the Future
Back to the Future Part II & III
Bad Dudes Vs. DragonNinja
Bad News Baseball
Bad Street Brawler
Ballon Fight
Bandai Golf: Challenge Pebble Beach
Bandit Kings Of Ancient China
Bard's Tale
Baseball
Baseball Simulator 1.000
Baseball Stars
Baseball Stars 2
Bases Loaded
Bases Loaded 2
Bases Loaded 3
Bases Loaded 4
Basewars
Batman
Batman Returns
Batman: Return Of The Joker
Battle Chess
The Battle Of Olympus
Battleship
Battletank
Battletoads
Battletoads & Double Dragon
Bee 52
Beetlejuice
Best Of The Best
Bible Adventures
Bible Buffet
Big Bird Hide & Speak
Big Foot
Big Nose Freaks Out
Big Nose The Caveman
Bill & Ted's Excellent Adventure
Bill Elliot NASCAR Challenge
Bill Elliot Super Off Road
Bionic Commando
The Black Bass
Blackjack
Blades Of Steel
Blaster Master
The Blue Marlin
The Blues Brothers
Bo Jackson Baseball
Bomberman
Bomberman 2
Bonk's Adventure
Boulder Dash
A Boy & His Blob
Break Time
Breakthru
Bubble Bath Babes
Bubble Bobble
Bubble Bobble 2
Bucky O'Hare
Bugs Bunny's Birthday Blowout
Bugs Bunny's Crazy Castle
Bump 'N' Jump
Burai Fighter
Burgertime
Cabal
Caesar's Palace
California Games
Captain America
Captain Comic
Captain Planet
Captain Skyhawk
Casino Kid
Casino Kid 2
Castelian
Castle Of Deceipt
Castle of Dragon
Castlequest
Castlevania
Castlevania II: Simon's Quest
Castlevania III: Dracula's Curse
Caveman Games
Challenge Of The Dragon
Championship Bowling
Championship Pool
Chase H.Q.
Cheetamen 2
Chessmaster
Chiller
Chubby Cherub
Circus Caper
City Connection
Clash At Demonhead
Classic Concentration
Cliffhanger
Clu Clu Land
Cobra Command
Cobra Triangle
Code Name: Viper
Color A Dinosaur
Commando
Conan
Conflict
Conquest Of The Crystal Palace
Contra
Contra Force
Cool World
Cowboy Kid
Crash 'n' The Boys Street Challenge
Crash Dummies
Crystal Mines
Crystalis
Cyberball
Cybernoid
Déjà Vù
Dance Aerobics
Darkman
Darkwing Duck
Dash Galaxy In The Alien Asylum
Day Dreamin' Davey
Days Of Thunder
Deadly Towers
Death Race
Deathbots
Defender 2
Defender of the Crown
Defenders Of Dynatron City
Demon Sword
Desert Commander
Destination: Earthstar
Destiny Of An Emperor
Dick Tracy
Die Hard
Dig Dug II
Digger T. Rock
Dirty Harry
Disney's Adventures In The Magic Kingdom
Disney's Duck Tales
Disney's Duck Tales 2
Disney's The Little Mermaid
Disney's The Rescue Rangers
Disney's The Rescue Rangers 2
Dizzy The Adventurer
Donkey Kong
Donkey Kong 3
Donkey Kong Classics
Donkey Kong Jr.
Donkey Kong Jr. Math
Double Dare
Double Dragon
Double Dragon II
Double Dragon III
Double Dribble
Double Strike
Dr. Chaos
Dr. Jekyll & Mr. Hyde
Dr. Mario
Dracula
Dragon Fighter
Dragon Power
Dragon Spirit
Dragon Warrior
Dragon Warrior II
Dragon Warrior III
Dragon Warrior IV
Dragon's Lair
Dragonstrike
Duck Hunt
Dudes With Attitude
Dungeon Magic
Dusty Diamond's All-Star Softball
Dynowarz
Eggsplode
Elevator Action
Elimonator: Boat Duel
Elite
The Empire Strikes Back
Everet & Lendel Top Players Tennis
Excitebike
Exodus
F-117 Stealth Fighter
F-15 City Wars
F-15 Strike Eagle
Family Feud
The Fantastic Adventures Of Dizzy
Fantasy Zone
Faria
Faxanadu
Felix The Cat
Ferrari Grand Prix
Fester's Quest
Final Fantasy
Fire Hawks
Fire N Ice
Firehouse Rescue
Fisher-Price: I Can Remember
Fisher-Price: Perfect Fit
Fist Of The North Star
Flight Of The Intruder
The Flintstones
The Flintstones: Surprise At Dino Rock
Flying Dragon: The Secret Scroll
Flying Warriors
Formula One: Built To Win
Frankenstein
Freedom Force
Friday The 13th
Fun House
G.I. Joe
G.I. Joe: The Atlantis Factor
Galactic Crusader
Galaga
Galaxy5000
Gargoyle's Quest 2
Gauntlet
Gauntlet 2
Gemfire
Genghis Khan
George Foreman KO Boxing
Ghost Lion
Ghostbusters
Ghostbusters 2
Ghosts & Goblins
Ghoul School
Gilligan's Island
Goal!
Goal! 2
Godzilla
Godzilla 2
Gold Medal Challenge 92
Golf
Golf Grand Slam
Golf Power
Golgo 13: Top Secret Episode
Goonies 2
Gotcha!
Gradius
Grand Prix
The Great Waldo Search
Gremlins 2: The New Batch
The Guardian Legend
Guerilla War
Gum Shoe
Gun Nac
Gunsmoke
Gyromite
Gyruss
The Harlem Globetrotters
Hatris
Heavy Barrel
Heavy Shreddin'
High Speed
Hillsfar
Hogan's Alley
Hollywood Squares
Home Alone
Home Alone 2
Hook
Hoops
Hot Slots
Hudson Hawk
The Hunt For Red October
Hydlide
Ice Climber
Ice Hockey
Ikari Warriors
Ikari Warriors 2
Ikari Warriors 3
Image Fight
Immortal
Impossible Mission 2
Indiana Jones & The Last Crusade
Indiana Jones & The Temple Of Doom
Indy Heat
Infiltrator
Iron Tank
Isolated Warrior
Jack Niklaus's Greatest 18 Holes Of Major Championship Golf
Jackal
Jackie Chan Kung Fu Heroes
James Bond Jr.
Jaws
Jeopardy!
Jeopardy! 25th Anniversary
Jeopardy! Junior Edition
Jetsons
Jimmy Connors Tennis
Joe And Mac
John Elway's Quarterback
Jordan vs. Bird: One on One
Joshua
Journey To Silius
Joust
Jungle Book
Jurassic Park
Kabuki Quantum Fighter
Karate Champ
Karate Kid
Karnov
Kickle Cubicle
Kickmaster
Kid Icarus
Kid Klown
Kid Kool
Kid Niki
King Neptune's Adventure
King Of Kings
King's Knight
King's Quest 5
Kings Of The Beach
Kirby's Adventure
Kiwi Kraze
Klash Ball
Klax
Knight Rider
Krazy Kreatures
Krion Conquest
Krusty's Fun House
Kung Fu
Kung Fu Heroes
L'Empereur
Laser Invasion
The Last Action Hero
Last Ninja
The Last Starfighter
Lee Trevino's Fighting Golf
Legacy Of The Wizard
The Legend Of Kage
The Legend Of Zelda
Legendary Wings
Legends Of The Diamond
Lemmings
Lethal Weapon 3
Life Force
Linus Spacehead
Little League Baseball
Little Nemo The Dream Master
Little Ninja Bros
Little Sampson
Lode Runner
The Lone Ranger
Loopz
Low 'G' Man
Lunar Pool
M.U.L.E.
M.U.S.C.L.E.
MC Kids
MIG-29
Mach Rider
Mad Max
The Mafat Conspiracy
Magic Darts
Magic Johnson's Fast Break
The Magic of Scheherazade
Magician
Magmax
Major League Baseball
Maniac Mansion
Mappyland
Marble Madness
Mario Bros.
Mario Is Missing
Mario Time Machine
Marvel's X-Men
Master Chu And The Drunkard Hu
Maxi 15
Mechanized Attack
Mega Man
Mega Man II
Mega Man III
Mega Man IV
Mega Man V
Mega Man VI
Menace Beach
Mendel Palace
Mermaids Of Atlantis
Metal Fighter
Metal Gear
Metal Gear 2: Snake's Revenge
Metal Mech
Metal Storm
Metroid
Michael Andretti's World Grand Prix
Mickey Mousecapade
Mickey's Adventure In Numberland
Mickey's Safari In Letterland
Micro Machines
Might And Magic
Mighty Bomb Jack
Mighty Final Fight
Mike Tyson's Punch Out!
Millipede
Milon's Secret Castle
Miracle Keyboard Teaching System
Mission Cobra
Mission: Impossible
Monopoly
Monster In My Pocket
Monster Party
Monster Truck Rally
Moon Ranger
Motor City Patrol
Ms. Pac-Man
Mutant Virus
Mystery Quest
NARC
NES Open Golf
NFL Football
Nigel Mansell-World Class Racing
Nightmare On Elm Street
Nightshade
Ninja Crusaders
Ninja Gaiden
Ninja Gaiden II: The Dark Sword Of Chaos
Ninja Gaiden III: The Ancient Ship Of Doom
Ninja Kid
Nobunaga's Ambition
Nobunaga's Ambition 2
North And South
Operation Wolf
Orb 3D
Othello
Over Horizon
Overlord
P'radikus Conflict
P.O.W.
Pac-Man
Pac-Mania
Palamedes
Panic Restaurant
Paperboy
Paperboy 2
Peek A Boo Poker
Pesterminator
Peter Pan And The Pirates
Pictionary
Pinball
Pinball Quest
Pinbot
Pipe Dream
Pirates!
Platoon
Play Action Football
Pool Radiance
Popeye
Power Blade
Power Blade 2
Power Punch 2
Predator
Prince Of Persia
Princess Tomato In The Salad Kingdom
Pro Sport Hockey
Pro Wrestling
Pugsley's Scavenger Hunt
Punch Out!!
Punisher
Puss 'N' Boots
Puzzle
Puzznic
Pyramid
Pyramids Of Ra
Q*Bert
Qix
Quattro Adventure
Quattro Arcade
Quattro Sports
R.B.I. Baseball
R.B.I. Baseball 2
R.B.I. Baseball 3
R.C. Pro-Am Racing
R.C. Pro-Am Racing 2
Race America
Racket Attack
Rad Racer
Rad Racer 2
Rad Racket
Raid 2020
Raid On Bungling Bay
Rainbow Island
Rally Bike
Rambo
Rampage
Rampart
Remote Control
Ren And Stimpy: Buckaroos
Renegade
Rescue: The Embassy Mission
Ring King
River City Ransom
Road Blasters
Road Runner
Robin Hood
Robo Demons
Robo Warriors
Robocop
Robocop 2
Robocop 3
Rock N Ball
Rocket Ranger
Rocketeer
Rockin' Kats
Rocky & Bullwinkle
Roger Clemens Baseball
Roller Games
Rollerball
Rollerblade Racer
Rolling Thunder
Romance Of The 3 Kingdoms
Romance of the 3 Kingdoms 2
Roundball
Rush N Attack
Rygar
SCAT
Scarabeus
Secret Scout
Section Z
Seicross
Sesame Street 1-2-3
Sesame Street 1-2-3/A-B-C
Sesame Street A-B-C
Sesame Street Countdown
Shadow Of The Ninja
Shadowgate
Shatterhand
Shingen the Ruler
Shinobi
Shockwave
Shooting Range
Short Order
Side Pocket
Silent Assault
Silent Service
Silk Worm
Silver Surfer
Simpsons: Bart Meets Radioactive Man
Simpsons: Bart Vs. The Space Mutants
Simpsons: Bart Vs. The World
Skate Or Die
Skate Or Die 2: The Search For Double Trouble
Ski Or Die
Skull & Crossbones
Sky Kid
Sky Shark
Slalom
Smash TV
Snake Rattle 'n' Roll
Snoopy's Silly Sports
Snow Bros.
Soccer
Solar Jetman
Solitaire
Solomon's Key
Solstice
Space Shuttle
Spelunker
Spiderman: Sinister 6
Spiritual Warfare
Spot The Game
Spy Hunter
Spy vs. Spy
Sqoon
Stack-Up
Stadium Events
Stanley
Star Force
Star Soldier
Star Trek: 25th Anniversary
Star Trek: The Next Generation
Star Voyager
Star Wars
Starship Hector
Startropics
Startropics II: Zoda's Revenge
Stealth ATF
Stinger
Street Cop
Street Fighter 2010
Strider
Stunt Kids
Sunday Funday
Super C
Super Cars
Super Dodge Ball
Super Glove Ball
Super Jeopardy
Super Mario Bros.
Super Mario Bros. 2
Super Mario Bros. 3
Super Pitfall
Super Spike V-Ball
Super Sprint
Super Spy Hunter
Super Team Games
Superman
Swamp Thing
Swordmaster
Swords & Serpents
T&C Surf Design
T&C Surf Design 2: Thrilla's Safari
Taboo, The 6th Sense
Tag Team Wrestling
Taggin Dragon
Tale Spin
Target: Renegade
Tecmo Baseball
Tecmo Bowl
Tecmo Bowl 2
Tecmo Cup Soccer
Tecmo NBA Basketball
Tecmo World Wrestling
Teenage Mutant Ninja Turtles
Teenage Mutant Ninja Turtles 2: The Arcade Game
Teenage Mutant Ninja Turtles 3: The Turtles Take Manhattan
Teenage Mutant Ninja Turtles: Tournament Fighters
Tennis
The Terminator
Terminator 2: Judgement Day
Terra Cresta
Tetris (I)
Tetris (II)
Tetris 2
Three Stooges
Thunder And Lightning
Thunderbirds
Thundercade
Tiger Heli
Tiles Of Fate
Time Lord
Times Of Lore
Tiny Toon Adventures
Tiny Toon Adventures 2
Tiny Toon Cartoon Workshop
To The Earth
Toki
Tom And Jerry
Tombs And Treasure
Toobin'
Top Gun
Top Gun II: The Second Mission
Total Recall
Totally Rad
Touchdown Fever
Toxic Crusaders
Track & Field
Track & Field 2
Treasure Master
Trick Shooting
Trog
Trojan
Trolls On Treasure Island
Twin Cobra
Twin Eagles
Ultima: Exodus
Ultima: Quest Of The Avatar
Ultima: Warriors Of Destiny
Ultimate Air Combat
Ultimate Basketball
Ultimate League Soccer
Ultimate Stuntman
Uncharted Waters
Uninvited
The Untouchables
Urban Champion
Vegas Dream
Venice Beach Volleyball
Vice: Project Doom
Videomation
Vindicators
Volleyball
WCW: World Championship Wrestling
WURM
WWF King Of The Ring
WWF Steel Cage
WWF Wrestlemania
WWF Wrestlemania Challenge
Wacky Races
Wall Street Kid
Wally Bear And The No! Gang
Wario's Woods
Wayne Gretzky Hockey
Wayne's World
Werewolf
Wheel Of Fortune
Wheel Of Fortune With Vanna White
Wheel Of Fortune: Family Edition
Wheel Of Fortune: Junior Edition
Where In Time Is Carmen Sandiego
Where's Waldo?
Who Framed Roger Rabbit?
Whomp'em
Widget
Wild Gunman
Willow
Win, Lose, Or Draw
Winter Games
Wizardry
Wizardry 2: Knight Of Diamonds
Wizards & Warriors
Wizards & Warriors 2: Ironsword
Wizards & Warriors 3
Wolverine
World Champ
World Class Track Meet
World Cup Soccer
World Games
Wrath Of The Black Manta
Wrecking Crew
XEXYZ
Xenophobe
Xevious
Yo! Noid
Yoshi
Yoshi's Cookie
Young Indy Chronicles
Zanac
Zelda II: The Adventure Of Link
Zen: Intergalactic Ninja

I have a very small collection of gameboy (And GBC) games:
Super Mario Land
Donkey Kong: Game Boy
Tetris
Pokemon Red & Blue
Kirby's Dream Land: Game Boy
Super Mario Land 2: The Six Golden Coins: Game Boy

Thats all for now, in part 2, N64 and PS2 games.