Come to think of it, Richard is his own worst enemy, so we're going to say he's both the protagonist and antagonist of the play. Remember when he has that "Ah-ha!" moment the night before the battle at Bosworth Field? He basically comes to realize what we (the audience) have known all along: he's the villain responsible for all the bad things about to happen to him:
O no, alas, I rather hate myself.
I am a villain. (5.5.1).
If Richard is our protagonist, then everyone who gets in his way is behaving like an antagonist. This includes Clarence, King Edward IV, and the young princes, who all have more of a right to the throne than Richard. Same goes for Margaret, who spends most of her time skulking around the castle hurling nasty curses at Richard (and everyone else). Even Richard's wingman, Buckingham, becomes an antagonist when he refuses to kill the little Princes for Richard. Basically, what we're saying is that everyone in this play is an antagonist.