So I have been friends with someone for more than eight years. Yes, we are pretty close and all, but recently, we always seem to have disagreements. I for one try to mend the things between us, but she is a person who doesn't accept correction. She chooses to ignore me instead, despite the efforts I have made to be close to her once more. I know that I should be more considerate, I always listen to her problems. (I never tell her mine, because one time, I did, and she told me that I was too self centered) What should I do?

sorry to say this but it's best to go and make new friends. She sounds like she's using you.

Well, friendship works two ways. If one wont put in effort to mend when the other does then theres no point in the friendship(?)

Sit down and have a talk? About the past and stuff? Maybe it may get her to cool off or something. But honestly if she openly shows that she really wants to cut off ties with you theres no helping it. Nothing much you can do.

Like >>3 said, friendship isn't a one-way deal. It's a mutual effort, and your friend just isn't giving back. However, you need to convey this to her before taking any drastic measures.
Explain to her that you feel she isn't putting effort into your friendship. A real friend, the kind of person that belongs in your life, would acknowledge your concerns and try to fix your relationship.

>>1 friends grow apart and it hurts but you need to move on and make new friends who will truly appreciate your company. You can always talk with her about it too, which is a good idea.