What kind of turtle do I have?

Well, I don't know where you're located, but it looks like a Florida Cooter to me. Despite the name they're all over the Eastern and Central South of the United States. I have Red Eared Sliders and the pattern on the arm looks similar, but the shell isn't the same. At a first glance because of the little jagged parts at the back I thought it could be a Common Map Turtle, but the bottom of its shell doesn't look like yours, and any other Map Turtle has a very spiny shell.

I just looked up Florida Cooter on Wikipedia, I really think this is your turtle:

http://en.wikipedia.org/wiki/Coastal_plain_cooter

Hope this helps!

It looks a lot like a map turtle or a slider.I would need to see its head.

that is a coastal plain cooter