I used to love watching this show, the characters are so memorable. I agree with most of the types that have been brought up. IMO:
Robin: ISTx 1w9 (?)(maybe 8w9 or 5w6?) sp/sx RCOEI - I've never been sure of Robin's type. ISTJ fits well enough, but to play the Devil's Advocate, why not ISTP? Ti/Se fits him much better than Si/Te, IMO. Same with Artisan over Guardian. He uses rash, on-the-fly manuevers in combat situations and thrives on adrenaline, displaying his prominent auxiliary Se. His analysis and ingenuity with plans behind the scenes, especially concerning Slade, seem very Ti, with the tertiary Ni coming into play as well.
Starfire: ENFP, possibly ENFJ. 7 so/sx SLUAI. There's no way she's an ESFJ, she doesn't have a drop of Si in her. ESFP I could see however. Her odd habits and observations could be as much a product of being an alien to earth as they could be manifestations of Ne. NF fits her quite well in general though.
Cyborg: ESTJ 6w7 so/sp SCOaN
Raven: INTJ, definitely. 5w4 sp/sx RCOEI
Beast Boy: ExFP 7w6 so/sx SLUAI. I would normally say he's an obvious ESFP but but after considering the arguments for ENFP, it's certainly possible.
Minor Characters:
Terra: ESFP 7 so/sx SLUAN
Slade: INTJ 5 sp/sx RCOEI
Aqualad: ISFP
Speedy: ESTP
Bumblebee: ESTJ
Gizmo: ENTP
Jinx: ENFP?