Super Smash Bros. on the N64. Probably spent more time on that game than any other since, between maxing out the single player as each character and playing round friends' houses. You can call me cheap, but I got Kirby down to a fine art. Since you asked, B+up smash move off the edge of a platform - the downwards hit, if timed right, would shoot your opponent directly downwards into oblivion.

Amiga: Civilization and Mega Lo Mania.

X-COM 1 & 2, Doom 2, Transport Tycoon Deluxe and Dune 2. I would play these today at a heartbeat, although I'd probably have to get health insurance before booting up Dune 2.

I'd have to say Legacy of Kain: Soul Reaver for PS1 left the biggest impression on me from any game I've played, it was just so ambitious for its time and never pulled any punches with dialogue or themes, which struck me greatly as a young teenager - finally seeing some “serious” content in a videogame.

Also it had a great many novel technical and gameplay features, such as a streaming world without noticeable load times and no permanent death penalty, in fact dying was central to the gameplay at times since in “spirit” mode the entire world geometry morphed and displaced, yeah that game was a masterpiece.

As far as earliest random videogame memories go, there was this game called "Rescue on Fractalus" for one of the first Atari's my brother had. Oh man, you'll just have to YouTube that one - that game used to scare the hell out of me while waiting to see if the dudes were gonna be aliens or not

Honourable mentions: Populous, Sim City, Max Payne, Tekken and of course Doom, Heretic, Quake, Duke3D, Shadow Warrior and Blood - after that mid 1990's to early 2000's PC "golden age of innovation" for me most games just seem the same. Or that could just be me turning into a bitter old man before my time.

Oh, also the original Tony Hawk's Pro Skater 1, that game for me has to be the definition of “easy to play, hard to master” - I mean the very first time I booted it up I could barely manage a few thousand points per 2 minute run, then after a few months of practice I'm getting a few million. That's like what, a factor of 200 improvement in my skill level or something A very satisfying purely “mechanical” game.

Crap the more I think about it the more I could add so I'll try stop here

The one game I can remember that I couldn't stop thinking about was Final Fantasy VII. The reason I think it had such an impact on me was because I couldn't figure out what was wrong with Cloud. I knew something was wrong (he was hearing voices and clutching his head at odd times for goodness sake) but I couldn't figure out what it was and it bothered me something awful. Plus, he was crossdressing in the middle of disc one (I didn't see that one coming at all). I loved the music and it fit the scenes and the game and mood so perfectly. But I really think the storyline is what hooked me. So original.

I came a little early before the Atari's and the NES ,
Metal Gear Solid 4 - not a childhood game, but still Kick ass.
Super Mario Galexy 2 again...

What makes Mario Bros. good anyway? ask anyone about video games, and they talk about Mario... Best Series in video game history? Most likely...

I loved Jak and Dexter, when I was about 12/13, and Ratchet and Clank!

still puzzles me why these games were soo good, and now no game matches them, yet when I play them again, they feel silly...

guess my imagination has turned to mature to enjoy the games anymore...

What I'm trying to do, is come up with a game concept that is just as memorable and enjoyable as Mario Bros, and all the other games you remember.
-A Platformer that suggest puzzles, mild combat, funny dialog, yet still appeals to more mature gamers... hmm...

Everything Zelda (loved and still love the gameboy zelda). Special place in my heart: Tetrisphere.

Crash Bandicoot! Went back to that game recently and it's actually really hard to get 100% on so I must have been good when I was wee, or had the patience to retry levels 213,813 times.

FFVII also. The story of that game will stay with me forever no doubt.

Rayman for PC DOS. Amazing graphics and awesome music. As a little kid it was difficult for me to play it at advanced levels; but then at teenage years I installed it again and went all the way, 100% protoons and levels.
The Rayman character danced and laughed, he had a personality. The levels were colorful. It was like an interactive cartoon.

Others I can think of are classics such as Super Mario 64, Banjo-Kazooie and LOZ - Ocarina of Time.

I'm so glad someone else shares my enthusiasm for the tunes in this game. It's a permanent part of my music collection. Oh, and those backgrounds!

Let's see, childhood games? Well, there's too many, honestly. I will say that back in the day I'd draw my own levels on paper that closely resembling levels from Megaman and Sonic--at different periods, though. I also once made a t-shirt with a character that looked like a cross between Rayman and Dynamite Headdy. Once in school, I showed of a VHS of the last boss fight from Gunstar Heroes. Then, there was that time in English class where I faked an interview with Hideo Kojima, around the time I played Metal Gear Solid--got a good grade, too.

Galaga
Kings Quest
Combat
Pacman

Super Mario Brothers
Legend of Zelda
Metroid