Your close games...

Apart from Super Nintendo classics, like Super Mario World and Donkey Kong Country. I hold Zeus: Master of Olympus and Total Annihilation real close to my heart. I shared many wonderful experiences with my brother with these games.

The one closest to me would probably be Metroid: Zero Mission (GBA). I put so many hours into it, and was super excited after I finally finished it.
For PC, maybe Microsoft Flight Simulator X? Not really a game which gives good experiences.. but whatever.
I know my favorite storyline I have found a game EVER would be Pokemon: Mystery Dungeon Explorers of Time (Sky wasn't out yet)
Dem plot twists

EDIT: I just remembered, when I was seriously little my first computer games were the TLC, Reader Rabbit.

Childhood? Hmm, those would be Aidem Media's games about this guy. :3

Is the veeeeeeeeeery first by any chance "Sands of time"? Or did you really mean first one? =)

Too many to name.

you kids name games such as Witcher 1 and think your cool, most of the old players still remember games such as Settlers (1-3) or even playing Doctor Mario on "ancient" (Pegasus) consoles

Pokemon Yellow.
Super Mario World, The Legend of Zelda: A Link to the Past, Donkey Kong Country... Those three I wasn't ever too great at, but I played them with my older brother sometimes, or I would just watch him play other times.
Portal, Fable - The Lost Chapters, Halo - Combat Evolved, those are some games I consider, possibly to be the best of all time.

An awful lot.
I played a lot of adventure games in the 90s, most memorable for me were Hero's Quest, Zak mcKracken and Day of the Tentacle

The one that comes in my mind is road rash(there were a lot of other cool games too, like contra, mario) and warcraft 3 multiplayer(dota, vampirism, Td, e.t.c)

Digimon World 1, Digimon Card Battle, Megaman X4 and Red Alert 2.

Gothic II

A couple that stick in my mind, though they are from my teens

Dune (or was it Dune 2, can't remember been so long)
Mechwarrior 1 though 3 (3 was my favorite even with the lag)
Quake 2
Total Annihilation

Quake II and Quake III arena
Tomb Raider 3
Megaman X4
Super mario
Sonic 3
Galaga
Roller coaster tycon 2/3
Resident Evil 3

and probably a lot more.

Black & White, Worms World Party and Re-Volt are the first that come to mind. Those are more "late" childhood. In the "earlier" childhood I recall playing Super Mario Bros and a bunch of other NES games but those didn't leave quite as much of a lasting impression as the other games I mentioned. :D
EDIT: Oh, yeah, also Warcraft 3. Dunno how I forgot that one.

Frogger (Atari 2600), Super Mario Bros., Bomberman, Battle City, Donkey Kong, Tetris, Duck Hunt, Excitebike, Dr Mario, Ice Climber, Galaxian, Lunar Ball, Balloon Fight, Circus Charlie, Felix the Cat, Contra, Pokemon Silver/Crystal, DuckTales, Spider-Man (2000 version), Toy Story 2, Bugs Bunny: Lost in Time, FIFA 96, WWF SmackDown!, Worms World Party, Walt Disney World Quest: Magical Racing Tour, Crash Bandicoot 3: Warped, Crash Team Racing, Gran Turismo 2, Need for Speed: High Stakes, Driver, Lemmings (DOS), Counter-Strike 1.6, Heroes of Might & Magic III, Re-Volt.

Day of the Tentacle: Maniac Mansion 2.
Full Trottle.
Doom.
Doom II.
Quake.
Duke Nukem 3D.

All the demos of random games that I downloaded off of CNET back in the day.

Just Cause 2

Before that, I didn't have a gaming computer and I played free online flash games, such as:
Raze 1/2/3
Strike Force Heroes 1/2
Crush the Castle 1/2
Chibi Knight
Descision 1/2
Sushi Cat 1/2/3
Kingdom Rush
Learn to Fly 1/2
Fisher-Diver
The Last Stand - Union City
Zombotron

...Aaaand a crapload of other games. This list barely scratches the surface.

Crash bandicoot and Spyro for sure. Then there are some random games like street fighter, die hard and LAPD: future cop which were awesome games.

Prince of Persia - original
Worms: Armageddon
Carmagedon
MiG 29 Fulcrum, F22 Lightning
Delta Force: Land Warrior and Black Hawk Down
Rainbow Six: Rogue Spear
Tomb Raider 2
Buggerman
Suppaplex
Quake 2
FIFA 2001
Heroes of Might & Magic 3
Driver
Test Drive
Need for Speed 3
Mortal Kombat triology

Spyro.

these are some from psx and ps2 that i spent lots and lots of hours playing:
-final fantasy tactics,vii,viii,ix,x
-breath of fire 4
-kingdom hearts 1,2
-shadow hearts 1,2
-devil may cry 1,2,3
-driver 1,2
-medievil 1,2
-resident evil 1,2,3

Pokemon Blue. I spent a whole summer trading pokemons and when I finally got the 151rst.. yeah. I was 6 and it felt amazing. Haven't restarted it to this day.

2D Prince of Persia was pretty neat. I also remember playing 2D Duke Nukem :D

Games that used to be (and still are, to some degree) really close to me would be
the original Dungeon Master,
Blood Omen (Legacy of Kain),
the first Gothic
and Vampire the Masquerade: Redemption.

Hmm, childhood games...

Well there were a lot of card games: euchre, spades, hearts, rummy, rook, Board games: checkers, chess. monopoly, backgammon, scrabble, Risk. Other games included kick-ball/tee-ball/base-ball tag/freeze tag, hide-n-seek, Ollie-Ollie-over, red rover, volleyball, basketball, crochet.