My list isn't in any particular order because I don't think I could ever figure out which game of these games is really better than the others; they are all incredibly good games in my opinion.
Counter-Strike - I might be a bit biased with this game. When I was 15 through about 17 years old, I did a bunch of LAN tournaments for this game with some friends of mine. So my experience of the game was enhanced by something other than the game itself. There are all sorts of servers out there that can change the game, from Deathmatch servers, Warcraft servers, knife/low gravity/crazy air acceleration servers, surf map servers, climb map servers, and hey, the default game is incredible all on it's own.
Warcraft III - I've been playing this game since it came out, too. It's extremely customizable, and it's been a source of all sorts of awesome stuff from custom maps. Hell, there's even a full stand-alone game in beta right now that is a clone of DoTA (
Heroes of Newerth). I even played WCIII game last week for some hero arena maps.
World of Warcraft - I know lots of people will say this is a terrible game, and I'd have to agree that it
can turn into a terrible game. It's all up to the player as to if it's going to be terrible or awesome. You don't have to grind for anything, ever, and that's a surefire way to make the game suck. I played with a bunch of friends, and we just screwed around the whole time, and it was a lot of fun. It didn't limit how far we could get in the game either. It's an easy game overall and doesn't take much to get to the top. It's a great game if you like the genre.
Command and Conquer: Red Alert Series - I'm not really a big fan of RTS games, but this is one of the few RTS games I had a lot of fun with.
Half-Life 1 mods - I guess Counter-Strike fits into this, too, but I thought Counter-Strike deserved its own spot on the list. Anyhow, there's just tons of great mods out there. Sven-Coop, Rocket Crowbar, Jailbreak, Day of Defeat, The Specialists, Firearms, Natural Selection, Team Fortress Classic, Pirates Vikings and Knights, Frontline Force, Paintball, Battlegrounds, Science and Industry, and the list just goes on and on.