Well, as many people have stated before myself it really comes down to what the person likes. If you prefer a more fantasy, or rpg style, or maybe you like shooting games.
Either way here's a few recommendations.
Runescape (simple and free)
World of warcraft
Aion (Released in September)
Silk Road Online (Free)
Knight online (Free)
Oblivion (Not multiplayer, but a GREAT game)
Half-life (1 or 2.. usually comes with counterstrike anyways)
Call of duty 4
Team Fortress 2
Left 4 dead.
There's a whole world of games out there, most of the games i recommended are meant for online play.