I have given second chances to two people in my life.
The first, a girl I was crazy in love, head over heals for, broke up with me because she was interested in another girl. When it didn't work out with her, she came back to me. I, ignorantly, thought she really wanted to make things work with me so I took her back. Things went on like that until I was on the fourth chance and I couldn't take it anymore.
The second time was my most recent ex-girlfriend. (Recent being over 3 years ago. lol) She cheated on me with a girl who is now my best friend, funny enough. Up to that point I had told myself that if anyone cheated on me it would be a deal breaker. But, I loved her. So when she asked for a second chance I gave it to her. We broke up less than a month later because I found out she was still cheating, this time with multiple people.
Despite my bad experiences, I would still give someone a second chance. It's just not in me to not try to make things work. I also feel that every relationship is a learning experience. So even though things ended badly in both cases, I don't regret the decisions I made because I learned a lot of things from both.