My favorite of all time was Asheron's Call. It was an MMO released in 1999 (IIRC) and I played from 2001-2005 or 2006ish. The game itself was great, but the community was the best part of the game. I still talk with a dozen of the people I used to play with.
Other than that, my favorites were:
Command & Conquer, C&C Red Alert
Diablo, Diablo II (I finally left when they segregated old characters from new characters, so I couldn't show off my 1.09 Grandfather, 2x 1.08 Vampire Gazes, etc. anymore, lol)
Starcraft, Warcraft III
Half-Life (for its time, I still prefer it to Half-Life II)
Civilization (original), Masters of Magic, Colonization
As a little kid, the NES and our original Tandy-something-or-other are what got me into games. Next it was the Super Nintendo and an Hewlett Packard Windows 95 Pentium II 266MHz, then an HP Pentium II 450MHz, then another HP - Pentium III 1GHz. By the time we got the Pentium III, I was the computer whiz in the family, and I convinced my parents to buy a Geforce 4 MX420 64MB so I could play something, but I don't remember what. From there, we got an HP 2.0GHz Pentium 4 that we had nothing but problems with, so we finally switched to Dell with a couple of 3.0GHz Northwoods. FINALLY, sometime around 2004ish, I ordered some parts and built my first "homemade" computer - X2 4200+, 1GB Corsair DDR 400, 6800 GT PCI-E, and an ASUS A8N-SLI Premium. Cost a pretty penny, and the addiction has only continued from there...