There are several species of snapping turtles found throughout North America and parts of Central and South America. The most common one kept in captivity is just the common snapping turtle. They're named for the powerful jaws that they have, and the snapping biting motion that they make when out of the water and feeling threatened. They also have a very long tail.
Some people do keep snapping turtles as pets. I recommend you don't keep the snapping turtle if you are new to reptile keeping. They can grow quite large. They require an aquatic habitat, a special diet, and due to the fact they have those powerful jaws, if they're not handled appropriately, they can actually do some damage with their bite.
They're also very long-lived. They can live 50 or more years, and if you're not able to provide a home for that long and adequate care, it's probably not a good choice for you as your startup turtle pet.