"Mudblood's a really foul name for someone who is Muggle-born – you know, non-magic parents. There are some wizards – like Malfoy's family – who think they're better than everyone else because they're what people call pure-blood… I mean, the rest of us know it doesn't make any difference at all."
—Ron Weasley explaining blood prejudice to Hermione Granger and Harry Potter
"a filthy blood traitor like her",
"Half-breed" may be an insulting, rather than proper, term. It is known to be highly offensive to centaurs, though this may only be because it is in fact incorrect; centaurs are their own non-human breed, rather than a mix of species. Centaur also took the phrase "near human intelligence" to be a great insult, as Dolores Umbridge found out the hard way.
"Nasty brat, standing there as bold as brass. Harry Potter, the boy who stopped the Dark Lord. Friend of mudbloods and blood-traitors alike."
—Kreacher when he first met Harry Potter in 12 Grimmauld Place
Insults from the Marauders Map to Severus Snape:
"Mr. Moony presents his compliments to Professor Snape and begs him to keep his abnormally large nose out of other people's business.
Mr. Prongs agrees with Mr. Moony and would like to add that Professor Snape is an ugly git.
Mr. Padfoot would like to register his astonishment that an idiot like that ever became a Professor.
Mr. Wormtail bids Professor Snape good day, and advises him to wash his hair, the slime-ball."
Harry Potter speculated at one point that Marcus Flint might have some Troll blood in him. However, this may simply have been an insult toward Flint's appearance.
Why so tense, Potter? My father and I have a bet, you see. See, I don't think you're going to last ten minutes in this tournament. He disagrees. He thinks you won't last five!
"Longbottom, if brains were gold, you'd be poorer than Weasley, and that's saying something."
"He looks like an omelette..."
Insult to Xenophilius Lovegood said by Muriel.
House elves consider an insult be offered payment for their services.
"Your Mom is so fat that her Patronus is a cake!"