Well there is really no such thing as the "best" game. its really a personal issue.
One great website is Miniclip.com. It has countless single/multi player games.
Search Google for MMORPG (
Massive Multiplayer Online Role-Playing Games).
My son's favorite MMORPG are Maplestory and FLYFF (fly for fun)
Also almost every PC/console game today comes with an online version that lets you play against/with other gamers.
cheers:)