Some of my players have expressed an interest in playing "monsters" and I would let them.

However, I'd basically use a situation similar to the TV show Angel, where that monster is cursed or somehow given back its soul and free will. But I'd also tack on an extra caveat, such as a Heavy Conscience or Filled with Remorse. Essentially, the worst thing you could do to a monster is to give it a conscience, a soul, and the full realization of all its horrific actions.

You could always throw in a big caveat, like "revert back into monster if you find true happiness" just to stick with my example.

You have to realize that a full blooded monster of any type really throws the power scale of the game, so you have to up some part of the game to match, or limit them somehow. It's up to you, the GM, to determine how to do that.