Everyone will have a different opinion about the affair and it depends on many factors whether or not you can forgive them.
I was in the same situation once and I left her no matter how painful it was.
She had cheated on me with a known friend and she only confessed it to me when one of my best friends found out and told her to tell me or he would tell me. She was cornered.
So she told me everything that she's sorry, she still loves me and doesn't want to lose me.
There are probably some out there who would forgive her and give her a second chance, but I'm not one of them. My view is both radical and simple: I gave her everything I could and if she cheats on me; she can't be the right one.
And also an opinion a lot of people share. I'm sorry you were on the receiving end once.