Man, this could get lengthy. I actually thought of 6 but they are all so memorable I have to mention them all.

Atari 2600 Pitfall 2
It’s the game that reallly turned me in to a gamer in a lot of ways. It was just as good as a lot of Nintendo games at that same time in the mid 80’s. Tought me that graphics are not everything.

Street Fighter II CE Turbo Hyper
Arcade game that I played more than any other game in my entire life. It got to the point where I would play the game to beat it using every single character, back to back, without losing a single round. I got pretty good at it. Thought me that a fighting game can become a classic.

Super Mario Bros. 3
It was the only game I remember playing all the way through and waiting like two weeks and playing through it again and being completely satisfied both times that I completed it. That game changed the entire dynamic of what makes an epic game, possibly the best original video game of all time.

Sega Saturn : Deathtank
Hidden game in Duke Nuken 3D. One of the most entertaining multiplayer party games ever created and not many people even know about it.

Sega Saturn 10 player Bomberman
The only way to play it is with a simultaneous 10 player tournament. Single best and most memorable gaming experience in which I ever participated.

Arcade: Virtua Racing... only game I remember playing so much that I held just about every single top time on every course every single day it was ever at the arcade. Was a single player upright version... A good friend and I would play it for hours and hours, trying to cut hundreds of seconds off of our best times. It was an epic game for it’s time.

And in case you’re wondering, yes I own all of these games.

Well, you asked for it:

First is probably Super Mario Bros. 3. It's the first game that I remember beating and beating again and it did not matter, I still wanted to play it yet again. Welcome to replay value.
Second one that stood out for me like this is SNES Super Mario Kart.
Next would be Doom and Doom II. That game cranked up what was possible and really expanded developers imaginations.
Next would be Street Fighter II Turbo in the arcades. I'm still pretty good at it.
Next would probably be the original Halo. That game single handedly changed the entire industry.

Collectively we are looking at thousands of hours that I've played these games.
Would be hard for me to choose a runner up to those 5... probably Smash Bros Melee on GC and Goleneye on N64.