In addition to the Sonic and Mario games I mentioned back in November last year, the FlashyOnlineGames.com site has some excellent retro computer and arcade games rendered in Flash so that you can play them online in your web browser for free!
Check out these absolutely classic 1980's computer games from the glory days of the Commodore C64, the Commodore Amiga, the Sinclair ZX Spectrum and other old-school home computer systems:
Great Giana Sisters
Jetpac
Nebulus
R-Type
And also check out these all-time great 1980's arcade games:
Defender
Space Invaders
Centipede
Missile Command
Frogger
Pac-Man