The ninja turtles are Malaclemys terrapin breed. At least that is what I think they are due to their appearance. Though most believe them to be common Red-Eared Sliders (which is a terrapin as well). A terrapin is a turtle living in fresh or brackish water, that also spend a lot of time on land. *nods*
While I believe them to be Malaclemys, it was revealed in the 90s during an interview that they are Red-Ear Sliders. The TMNT craze among kids during that time caused a lot of this breed to be bred and then released into local ponds and lakes, making them a pest as time went on.
Tokka from the movie and Slash from the comics/cartoon were Alligator Snapping turtles.