If you girlfriend cheated on you with her ex but says she is sorry and pleads to go back with you what do you do?

You could understand that everyone makes mistakes now and then, sometimes really big ones. But that doesn't mean that she doesn't regret it or that she doesn't care about you. Perhaps it would be worth giving her a second chance? But if you do take her back, let her know she's forgiven and refrain from throwing it in her face should you get in an argument or something.