If you have one for single player and another for multiplayer, please list them both. Also please include the platform you played it on. I'll go first:

Single: Uncharted 2
Multi: COD: Modern Warfare 2

Both for PS3.

I tend to like turn-based strategy games, and I like best the ones that have replayability:

Civilization III is probably the one I've played the most (even after buying Civ IV).

Single: Final Fantasy VI
Multi: Street Fighter IV

I have to break it down one more category; PC and console. Morrowind on PC, and Uncharted 2 on console. Morrowind sucked me in for years, literally. Extremely immersive, and player-created content kept it constantly fresh. The graphics and physics don't hold up well today, and there's a lot of text to read instead of voice acting, but it's still my top all time. Oblivion, the games sequel, is right behind. Uncharted 2 doesn't have the open world or replayability of those games, but it's just so much fun, with a terrific story, that it doesn't really matter. Great stuff.

Multiplayer would be Unreal Tournament, the only MP game I ever got into for any length of time. I actually got damn good at it. Haven't played very many others; too many cheaters and campers ruin it for me.

It was all downhill from here.

The most satisfying gaming experience I've ever had was the original Half-Life by Valve Software for the PC.

Blizzard's WarCraft III RTS comes in as a very close second.

Age of Empires 1 and 2 have had the most replay entertainment for me over the years. To this day, I still play AoE.

Uncharted. I'm a little into Uncharted 2 and that looks to top it!

Wouldn't be surprised if it does. I loved the first one and was floored by the second.

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I love Duke's echo posts.

I'm not sure why this browser sometimes duplicates posts! I can't figure it out. Never had that problem on another form.

Dragon Age. Final Fantasy VI and VII. Street Fighter II HF and Street Fighter IV.

Super Metroid. Secret of Monkey Island. Space Quest III.

Star Control II. Rock Band 2. Knights of the Old Republic.

I have a lot of favorites.

I really liked Jedi Academy.

Castlevania: Symphony of the Night on PS1 for me.

For multi-player games, I'd probably have to say either the Rock Band series or Madden 97, a sentimental favorite.

This is one of those questions I simply can't answer, because I firmly believe that games are still evolving at a fairly rapid rate. No matter how brilliant a game is today, returning to it a few years later will magnify limitations and flaws of the game. Half-Life 2 was an awesome experience, but my attempt to play through it again resulted me in noticing how often characters spent forever chattering away while I hopped around the room in an effort to not be totally bored.

Maybe one day people will be buying 10 year old games and judging them by the exact same standards as a modern game.

Story was lacking, but I liked that it actually started you off as a Jedi. Early Jedi Knight 1 & 2 levels are always a bit of a pain to replay because the game is just so much more fun when the powers kick in.

The original C64 Rool of Radiance, Followed closely by Ultima III, then Baldur's Gate.

I did love the hell out of the N64 Royla Rumble game, And My favorite Arcade Game of all time is the original Matt Mania.

On the PC side (Mac, in my case), I love the Escape Velocity series from Ambrosia Software -- I especially liked the last iteration, Escape Velocity Nova. I also played the hell out of Sim City 2000, Civilization 3 and Baldur's Gate back in the day. I'm really fond of Assassin's Creed 2, Batman: Arkham Asylum and The Godfather on console (I've been playing all three on PS3).

And in the old arcade days, I was a Pac Man, Crazy Climber, Gorf, Joust, Scramble and Moon Patrol fanatic. Oh, and Dragon's Lair.

Escape Velocity was pretty good.
And SimCity 2000 and Civ III may have been the best versions of those games.

For old arcade games, I played quite a bit of Mr. Do, but enjoyed Ms. Pac Man more than Pac Man,
ans was quite fond of Joust and Defender, also liked Scramble there for awhile, too. Many others.
But, if I were to buy one now just to have one, it would be Mr. Do.

I almost put down Symphony of the Night. A flawless game.

It really is. Beautiful graphics and wonderful music---the only video game soundtrack I've ever bought.