Raging Bull
Goodfellas
Casino
Mean Streets
After Hours
Taxi Driver
Cape Fear
King of Comedy

That's in the order of "my favorites", but I rate "Mean Streets" as a better film than "Casino". I just like "Casino" better because of the subject matter.

And I agree with Ragging Bull about "After Hours". I'm not as gushing with my praise over it, but it is very under-rated and I highly recommend it.

Thing is, though, I think you have to be a New Yorker to truly appreciate it entirely.