That's more or less up to what you. If you want to have a goal of collecting every item in the game, then you do that. If you want to have a goal of playing through HC untwinked, then you do that. If you want to have a goal of having one of the best pvp characters on your realm, then you do that. If you just want to MF to your hearts content, or play every class through Hell, then you do that.
There's no real answer to "what are the goals" beyond killing the Prime Evils. Actual game-play related, there is Uber Trist. However, I'm not sure if Uber Trist is really in Diablo continuity, or just an added challenge for the players, so it may not not really be a "goal" in the game really.