I realize this thread is in the "console gaming" forum when it could be in either PC or console, but I'm surprised that no one has mentioned WoW or Warcraft 3/3x. In addition to the standard Warcraft 3, Dota is also an amazing game. It's spawned clone F2P League of Legends is one of my top 10 as well.
A lot of my games are on other people's lists already.
Secret of Mana
UT99
Counterstrike
SC/BW
D2/D2x
War 3
TF2
Games no one has mentioned:
Spawn: In the Demon's Edge (2000) - This was an Arcade game that was also released on dreamcast, mostly a 3rd person view fighting shooter. Although it played like a shooter, it was really a fighting game. It allowed for up to 4 arcade systems to be locally linked together, and you have nooo idea how much fun this was

It was made by capcom, so for a fighting game, it was fairly balanced. The single player boss time attack is lame IMO, the multiplayer is where this game shines, and it is truly an unnoticed gem for fighting game fans.
Wolfenstein: Enemy Territory 2003/2004 - for PC, free, multiplayer, objective based (think Assault in UT99, Rush in BFBC2 but with relevant, cool objectives, not just "blow up the box) fps. There were also a few "limited lives" server as well, which changed the tactics to a sense

Because it's multiplayer only, few people play this anymore, but people do since it's free.
Final Fantasy Tactics Advance 2 for DS - Someone mentioned FFT, but FFTA2 was the best of the series
Tactics Ogre: The Knight of Lodis (GBA) - Another isometric grid turn based strategy RPG similar to FFT. I absolutely loved this game more than any other turn based strategy. I also really, really enjoyed the story and RPG factor as well. This is one of the few games I've played through multiple times, once straight through, another time for all the unlocks/achievements (even back in 2002), and other times powered through for multiple endings.
Street Fighter 3 - 3rd Strike - Most balanced, in-depth SF fighting game ever to me. The removal of the parry mechanic from SF3 was a huge step backwards in SF 4 to me IMO. People talked about SF4 going "back to basics," but I felt SF4 lost huge depth.
Pokemon games for Gameboy - Childish and simple yes. Disturbingly fun as well. I have only played two fully (Blue for GB and Ruby for GBA). Haven't spent more than 5hrs in whichever DS version I have.
Star Wars Jedi Knight 2 - I only played the multiplayer, which was amazingly fun, but I'm told the single player was great too. Maybe this isn't quite top 10, but I spent many, many, many hours of fun playing this.
Marvel vs Capcom 2 - Not top 10 but top 20 for sure.