My cockatoo has bit me twice, not very hard at all, and both completely my fault when he didn't trust me and I was purposefully pushing limits. He goes after people in the house now though, but often just lunges.
My tiel nips a bunch, but that's because she is such a nervous bird with such low confidence. If you handle her right, she won't bite. She doesn't draw blood.
My sister's GCC is a terror due to the socialization.

But, again, another hormonal female that when handeled right can be a total dream. We're working on it.
LOL this sounds so bad - my birds really aren't so bad! But all in all, a bird will bite, and my guys have and some will if you really bother them.