I like the Benko gambit.
sharp responds to 1.d4?

Some good choices are: Semi-Slav, Leningrad Dutch, Benko Gambit, Blumenfeld Gambit, King's Indian Defence, Modern Benoni, and the Grunfeld.
My favourite to analyze is probably the Semi-Slav, especially after white plays 5.Bg5. Unfortunately, white can make the game boring if he avoids it or the Meran variation, often with the exchange Slav or 6.Qc2 without 7.g4. The Leningrad dutch is probably the best choice if you need to fight for a win at all costs, as there aren't really any forced drawing lines or exchange variations.

I play the Leningrad Dutch sometimes. I always feel like I'm hanging by a thread, even in the games that I win with it. It does lead to sharp, out of the ordinary positions that are fun to play.
@Fiveofswords: I was just about to mention those two along with the Chigorin Defense. I personally don't see how you can call anything else sharp without having those three in the discussion.

nobody ever mentions the budapest or albin counter gambit when people ask this....why?
There are people who like those gambits; what to recommend in my opinion depends on white's rating.

Either the Modern Benoni, Leningrad Dutch, KID are good choices. The Semi-Slav is also sharp if white plays the Botvinnik variation or Meran variation but white can just play the 6. Qc2 sideline and avoid both. Even in the Modern Benoni, white can play Nf3 instead of d5 after you play c5 and transpose into a quiet variation of the English opening. Like BigTy said, playing the Leningrad Dutch is a good way to ensure an unbalanced, sharp game.

Benko Gambit, Modern Benoni, Dutch Stonewall, QGD Noteboom and QGD Semi-Slav especially if white answers 5.Bg5.

it's easy to use budapest gambit when white use d4.
Easy, sure, but why would you want to?
here is my personal favourite from the modern defence. post others you know :)