The game is fucking amazing...so far, here are the missions I have done (don't worry, I won't give away any spoilers):
1. The Getaway, where you have to escape some rival mob guys.
2. Some random stuff with escorting people in the taxi...after all, you are a cabbie!
3. Joining the Salieri family (WOOHOO!!!).
4. Torching some cars (a la Goodfellas!).
5. Collecting protection money.
6. The mission I'm on now: a racing one...

These missions are superbly made...I LOVE THIS GAME!!!

GTA3 still has a special place in my heart, though...in fact, I'm working on completing it again! It's just that goddamn fun!