I'm keeping it strictly PC here, hoping GOG.com might pick up on it...
1. Grand Prix 2
When it came out it was cutting edge. Gorgeous graphics, good AI, lots of car setup options. And time has treated it very well with hundreds of custom carsets simulating all the seasons from the 50's till now. I still play it and prefer it above parts 1, 3 and 4.
2. Civilization series (including Colonization and Alpha Centauri
Turn-based strategy doesn't get better than this. No, it really doesn't.
3. Caesar III and Pharaoh
These two games are really, really good. Sim City in historic times with actual usable, direct feedback from your populace. Add a splash of war, a good trading system and Pharaoh's humongous monuments and you've got a winner!

Xcom UFO defence:
One of the best strategy games ever ...taking a squad into a terror site
still gives me the creeps ;-)
Researching alien technologie , building bases , and visiting mars.
Xcom has it all.
Elite 2 Frontier:
Davis Braben is a genius ...when this game first came out it was on 2 1.44 mb disks
He coded the entire milky way on to 2 disks under 3mb
Stars with orbiting planets ...complete with moons ...you could land on planets and moons
to mine ...or look for some asteroids ...scoop gas from gas giants.
And do anything your hearth desired.
Awesome game ...that has not been surpassed to this day.
Dungeon Master:
If you want a game that made the gameword tremble ...you need Dungeon Master.
At a time when most RPG where text based ascii coded programs.
FTL came with a game that was colorfull and immersive like nothing ever seen before
Enter a dungeon with a group of heroes ....and fight you way down collecting weapons
food and drinks for your heroes , powerfull armor,spells and potions.
Solving puzzles drawing maps ( no ingame map ...hardcore ^^ )
This game is a pure gem .
My 3 all time favorits.
Gaming since 1971

1) Planescape Torment--You can't beat the storyline and the characters.
2) Baldur's Gate Series(all 4 games, not Dark Alliance)--My first RPG, got me into dungeons and dragons, another hard to beat storyline
3) Neverwinter Nights (am I a d&d nut or something?) another unbeatable storyline with good playability, virtually limitless mods, and even online MMO like worlds
Honorable Mention:
Quake 2--Who doesn't love this FPS?
Icewind Dale--less on the storyline but still fun
Fallout--Uber story, fun to play, and targetted shooting(what more could you ask for)
Portal

I prefer Caesar 2 to 3 :)
As to a top 3, that's impossible!
A few games:
-> 7 kingdoms
-> Age of Empires 2
-> Anno 1602
-> Broken Sword
-> Call of Duty
-> Carmageddon
-> Caesar 2
-> Diablo 2
-> The longest Journey
-> Majesty: The Fantasy Kingdom (playing it again right now :))
-> Max Payne
-> Mohaa
-> Monkey Island
-> Planescape Torment
-> Return to Castle Wolfenstein (multiplayer that is)
-> Soldiers: Heroes of WW2
-> Star Wars: Kotor
-> Starcraft
-> World of warcraft (I put more time in this game then all other games combined)
That pretty much sums up the classic games I played these last 10 years. Picking a top 3 would just be evil to the other games, Blizzard alone has 3 games in the list.

In no order:
Severance: Blade of Darkness. (Misplaced at a housemove, and it was impossible to get hold of after, damnit, wouldve played it still).
Planescape: Torment. Perfect in every regard, except for the D&D system it is built on.
Lands of Lore. I actually used to sit and watch a friend play this, before I could get a comp that could play it myself.. But never managed to finish it, so it would be my most wanted game to show up here, at any rate ;)
Honorable mentions:
UFO-games
Warcraft 2
Dark Omen
Chaos Gate
Fantasy General (especially the multiplayer bit was just wicked)
Eye of the Beholder 2
Warlords 2&3 (hotseat)
Heroes of Might and Magic 2 (hotseat only)
Moonstone

lets for pc one then (hi to the community, im new)
Rollcage stage II
Planescape : Torment
Darkreign I and II

That's a tough one, but I think that:
1. Whole Heroes of Might and Magic series with except of part number 4
Literally whole days and nights in a row spent on that - since high school up until now
2. Diablo
Game that makes my heart jump and breath quicken, basically all the time
3. Baldur's Gate
Wonderful scenario and great character development
And recent favourite: The Witcher - Sapkowski and his world rules it all
And there are so many more....

1) Team Fortress 2
I've been thinking "Aw, it's just the hype, it probably won't really be my favorite game in the long run" but I've had the game since the beta (almost a full year now) and I've been consistently playing it the whole time. Probably the longest I've gone without playing TF2 at all is 1-2 weeks at the most since its beta release.
2) Diablo 2
Talk about a desert island game here. It just has so much depth to it. There are so many different ways to play every character, and such an amazing variety in the items to loot... I haven't even tried online play and this still goes as one of my all-time favorites! I would try online play, but I don't really want to go on with strangers. I think it would be more fun to play with a group of friends that I really know, but I just can't get anyone into it, or I can't meet anybody who already plays it. I've played lots of games that have tried to mimic Diablo 2, and it's pretty funny that none of them really do quite as good a job as this one.
3) Jets 'n' Guns Gold
I got this one for free in a giveaway a year or two ago, and even though I don't really regularly play it much anymore, it's just a really great game. Stylish in all the graphics and gameplay, and its soundtrack by Machinae Supremacy is pretty nice too.

Naming just three fav games is really hard, but my 3 would be
1.System Shock2
2. Deus Ex
3.Daggerfall

1. Elite - (C64)
2. Half Life - (PC)
3. Mass Effect - (PC)
And the rest really is history.

1) Planescape: Torment. Definitely. It shouldn't even be considered a game, since it's a masterpiece. Screenplay and character design cannot be compared to anything else. Graphics still looks good and music by Mike Morgan gives appropriate feelings of both an epic journey and a weird, dirty world. Torment gave me hope that cRPGs can really be up to great books standards when it comes to atmosphere and deep. Unfortunately, I haven't found any other cRPG like it. Every game in Torment ends with a painful thought about gaming industry.
2) Fahrenheit, known as Indigo Prophecy in USA. While Torment can be compared to a great book, Fahrenheit is done in resemblance to movie. It has a well-written dialogues and good voice acting. The screenplay has a few flaws, but overall it's cosistent and enjoyable. The greatest thing in Fahrenheit, though, is a climax it builds up, from the very first scene right to an end. It never lets you get bored, you're developing your own simpathies towards characters. Game is rather short unfortunately, leaving you wanting more.
I don't have my third fav yet. It would be easy to pick up something from the games I like, but I think they all lack something that would make them playable every single day. Though i haven't played a big portion of good stuff yet, and I'm eager to found some at gog.com.

PC only:
1. Quake III
I'm a sucker for shooters, especially the Quake series. I could name a million reasons why other shooters are "better" and Quake is worse, but yet for some reason I can't explain I still enjoy Quake more. It just FEELS better to rocket someone into gibs in Quake. It's hard to get my friends to even try Quake, but once they do good times are had by all.
2. Civilization series
This is the only series I like micromanaging in. In other strategy games I'm pretty lazy, but this I enjoy to the fullest. Most of the time I don't even get to the "end" of the game, I just build my civilization into a massive, wealthy, cultural powerhouse until it's way past bedtime.
3. Half Life 2
I really enjoyed Half Life, but the outdoor segments looked really bad due to technology restrictions. Half Life 2 fixed that and gave me some beautiful outdoor spaces. I have nothing to complain about now. Their formula of fighting > puzzle > fighting > puzzle is perfectly tuned so I don't get sick of either. For some reason though I really like the low-fidelity sounds of Half Life.
Consoles:
1. Sonic 2:
This is the best old-school Sonic. It was bigger and more polished than Sonic 1, it had a great soundtrack, and it had multiple ways to reach the end of a level. I almost never "beat" this game either, but it was enough to spend an hour or two and get near the end, enjoying the ride.
2. Katamari Damacy:
Holy crap, this had an amazing soundtrack. Of course, the whole rolling objects up from 1cm to continent-size was a really cool gameplay idea, but I knew I would have gotten bored with it eventually had they not put in such crazy good songs! There's so many styles--not just stereotypical Jpop. This is the one of only two game soundtracks I've ever considered buying on CD.
3. Megaman 64
Okay, it's a port of Megaman Legends, but I never had an original Playstation. What made this stick though, besides the pretty solid gameplay, is the story. I was 10 or so, and I was amazed that a game had voice overs, and moving lips to boot! This is the game that got me to stop watching tv shows for a good while. It was probably also the first time I fantasized about game characters, I so wanted Megaman and Tron Bonne to get it on. =p

System Shock 2...
Best...game...ever!
Warcraft 2...
Who wasn't addicted to this game?
Thief...
Do I even need to say any more?

1.Deus Ex
2.Deus Ex 2
3.Tie between: Fallout 1 and 2

1) Civilization Series -- no explanation is needed.
2) Quest for Glory series -- hilarious and at the same time dramatic storyline combined with top notch adventure/rpg hybrid gameplay.
3) Wing Commander: Privateer -- jettisoned the linear storytelling of virtually every other space combat game. Open ended enough where I could set my own goals, and participate in the surprisingly immersive story if I so chose.