I have played so many great games over the years, it's hard to pick just 3. But the 3 games that have had the biggest impact on me were:
1.Ultima Underworld
2. Planescape Torment
3. Baldur's Gate 2
Yeah, I like RPGs :P

In no particular order:
1. diablo ii w LOD
2. thief 1/2
3. oblivion - heavily modded

No order:
Ultima 6 or 7 (PC) Side note: EA encouraged you to make backup copies of your game disc, how times have changed!
Final Fantasy 1 (NES)
Xenogears (PSX)

Yeah, most of the major game companies recommended that. Floppy's degraded so easily you almost had to.

Furthermore, there were games with self-modifying code like the PC versions of Starflight 1 and 2 that could possibly be changed forever if you DIDN'T back them up. In my experiences with the first game, at least, if I decided to quit a game without saving, upon trying to start the game again, it would not load my last save or get into gameplay at all! (It makes me wonder why they even had that menu option in the first place.) I had to invoke another .COM file in the game folder to restore a saved game before I could play again-that is, if I did make a save!

Hmm . . .can I cheat? Well, I guess I'm going to cheat 'cause there's no way I'm just going to be able to list only 3 anyways;
1. Falllout 1(PC)
2. River City Ransom(NES)
3. Silent Storm(PC)
4. Vagrant Story(PS)
5. Counter-strike(PC)
6. Odin Sphere(PS2)
Off the top of my head

how?

3. Tomb Raider Series - Particularly 3. One of the first games I can remember playing. I was young enough at that point that tigers running from behind things at me scared me senseless, heh. But lots of guns, puzzles, and a slight m
2. Baldur's Gate 1 & 2 - I love RPGs. Need I say more?
1. Legacy of Kain: Soul Reaver (1)- I loved the music, I loved the bosses, I loved the whole setting, and most of all, I loved eating the souls of anyone (Or anything) getting in my way. That, and I've always had a soft spot for anything with Vampires.

By genre because like most people I really can't pick just 3:
RPG:
Planescape: Torment
Fallout 2 (yes, I like 2 better than 1. Heresy, I know)
Betrayal At Krondor
FPS:
System Shock 2
Deus Ex
S.T.A.L.K.E.R.
Space Sim
Freespace 2
Independence War 2: Edge of Chaos
Independence War
Adventure:
Gabriel Knight
Quest For Glory 4
Grim Fandango

1. Fallout 1/2
2. Planescape: Torment
3. Baldur's Gate 2
I'm dedicated RPGs player. From non-rpgs strangly I would say Tony Hawk's Pro Skater 2 (Dont know why this game gave me so much fun since I've never even tried skateboarding)

1.Grim Fandango (PC)
2.Okami (PS2)
3.Half Life 2 (PC)
4.MediEvil (PS1)
5.Curse of Monkey Island (PC)
(I couldn't name 3! Too few! Also as you can see I am a fan of Sony consoles and the PC (I like old Nintendo consoles too). These aren't in order, apart from Grim Fandango which is my favourite game of all time).

1. Broken Sword 1&2 (PC) - Brilliant point 'n' click games.
2. Elasto Mania (PC) - 2D Stunt Bike game with great physics. Very addictive.
3. Striker (Spectrum) - Score goals and become a top European striker. Played it for years.

Three, you like to make it hard :)
I guess I would narrow it down to:
1) Ultima IV
2) System Shock
3) Diablo II

1. Arcanum (PC)
2. Metal Slug 2 (NeoGeo)
3. Diablo 2 (PC)

Just 3 out of so many years, and so many games? Hard choice. :)
But i'd say:
1. Civilization : greatest game concept ever, and by far the game i've played the most if you count all versions
2. Baldur's Gate : the best RPG i've ever played, though Fallout and Planescape Torment could go there as well
3. Deus Ex : is any explanation necessary? The perfect blend of FPS and RPG. System Shock is a very good substitute