Richard III makes a pretty big deal out of sex. In his opening speech he complains to the audience that since war has given way to peace, everyone in England has been busy hooking up. Everyone except for him, that is.
Why's that? Well, Richard tells us that he's not very attractive and was born "deformed, unfinish'd" and "scarce half made up" (1.1.1). A lot of scholars read this simply as Richard's way of telling us that he's got some physical deformities (like being a "hunchback"). Others see a more specific and bawdy meaning in this speech. According to Pauline Kiernan (author of Filthy Shakespeare), when Richard tells us he's been "cheated by nature" and "cannot prove a lover," he's basically saying that he's sexually inadequate because he's missing some key anatomical parts.
The funny thing is, even though Richard tells us he's got some shortcomings in the love department and has zero game with the ladies, the guy manages to woo Lady Anne after killing her husband and father-in-law. While he's putting the moves on this grieving widow, he brags that he can't wait to marry her so he can get her in bed (1.2). Obviously, this character is meant to have some sex appeal, which is why the role has often been given to good-looking actors like Sir Laurence Olivier (who was considered a hottie back in the day). We have to admit that when Richard is played by the right actor, he's pretty seductive, despite the fact that other characters refer to him as an "elvish-mark'd, abortive, rooting hog" and a "poisonous bunchback'd toad."
So is Richard just yanking our chain when he says he's "not shaped for sportive tricks, / Nor made to court an amorous looking-glass" (1.1.1)? You decide.