My ex wants to be friends

Long story short, my first girlfriend I ever had cheated on me a few months after we started dating. It completely ruined me, and actually pushed me to the point of depression. She had broken my heart and didn't even care. She's the main reason why I couldn't trust my other exes that much, and the reason why I have a hard time talking to girls.
But, she had recently been trying to talk to me as if nothing had happened between us, like the whole incident never happened. I'm not quite sure if I want to forgive her just yet, or just blow her off almost like she did to me for the few months after it happened. I just need some help.

Well it all depends on how you feel. Obviously this girl caused a lot of problems for you. Maybe more than she realized. You were really hurt by what she did and now you have trust issues with everyone you date.
Dating is all about trust, if there is no trust, there is no relationship. In order to have a healthy relationship with someone you need to be able to trust them and they you. You are afraid of trusting someone because you don't want to get hurt again, but being in a relationship that is a risk you choose to take. If you are not willing to take that risk you are not ready for a new relationship.
Another thing is you are taking what your ex girlfriend did to you and basically foreshadowing it on every girl you meet. Every person is different and you can't assume that all women are untrustworthy.
From how it sounds it doesn't seem like you are ready to be friends with your ex because you are still very hurt and it's pretty inconsiderate of her to talk to you as if nothing happened. She could at least apologize.
I think you need to look at this relationship you had an really evaluate it, learn from it and most importantly put it behind you. It would be pretty hard to move on from the relationship if you are friends with your ex. Everyone goes through break up's and everyone gets their heart broken sometime in their life. After you're completely over the relationship you will feel so much better and then maybe you'll be ready to date again! I hope you learn from the experience and become happier and focus on yourself for now.