What is a very good online game

that depends on what style of games you like

if you like shooters with multipule people (more than 4) then M.W.2 (modern warfare 2)
if you like to do co-op then Resident Evil 5 (either regular or gold edition [gold edition you get all expansion packs])

Racing you have pretty much burnout, need for speed, etc.

Mx/Atv games

there arnt really any MMO's YET for ps3 (soon to have FFXIV [final fantasy 14])