Centaurs are basically half-human, half-horse. Though wizards would consider them beings, centaurs prefer to be called beasts, so that's what they're classified as.
They live in forests and they're super-intelligent. They also don't like Muggles much. Or wizards. They tend to keep to themselves actually. Their lives are pretty mysterious and that's just the way they like it.
(Harry Potter book shout out: We first meet the centaurs in Harry Potter and the Sorcerer's Stone when Harry is serving detention in the Forbidden Forest. They pop up throughout the rest of the series.)
A Chimaera is a bit of a mash-up—it has a lion's head, a goat's body, and a dragon's tail. Eww.
Only one wizard has ever defeated a Chimaera…and that didn't work out so well for him in the end. He should have held on a little tighter to his Pegasus, if you know what we mean. (Hint: we're talking about a famous old Greek named Bellerophon.)
These tiny parasites are like little crabs (eww) with big fangs (double eww).
They like to infest the feathers of magical creatures or gnaw through wands or dirty cauldrons.
You can get rid of them with all kinds of potions. Has anyone invented Chizpurfle-Be-Gone yet?
Clabberts originated in America and look kind of like a cross between a frog and a monkey. The most interesting thing about it is the giant red pustule on its forehead that flashes red when there's danger around.
American wizards used to like keeping Clabberts in their gardens, but the practice got banned when too many Muggles saw the flashing lights and wondered what exactly was up. What indeed.
Crups look exactly like Jack Russell terriers except for one thing—their forked tails. They also really hate Muggles.
Wizards can keep Crups as pets as long as they get a license from the Ministry of Magic and perform a painless Severing Charm to get rid of that weird tail. We can't have the Muggles picking up on the magical dogs, now can we?