If you remember you orginal email that you used for Game Center and the name that it was under (usually your real name that you use for Itunes) go to https://appleid.apple.com/ then to get the password reset. Later go back to Game Center and USE your original email plus your new resetted password to log in, YOU DON'T NEED your Apple ID to log into Game Center. This has worked for me. NOTE: your email for resetting the password will have the name you have that email address attached to.
If you DON'T remember what email you used, then go to your actual account and see what email you have listed under your real apple ID.
Go here to see your account: https://appleid.apple.com/cgi-bin/WebObjects/MyAppleId.woa/227/wo/ySTFnwnuAkjyTx aE4tPw40/24.0.35.145.1.0.8
If those emails don't look familar to you or you've used another email address, at least at that point you can do the elimination process and try to figure out what other email addresses you've used.
If you STILL DON'T remember what email you used then do this:
1. Go into Game Center log in with your Apple ID and password like you do for Itunes.
2. Create a new account
3. When you get to the add email section then add an email a time to see if it takes it. If it doesn't then it will say that this email belongs to another Apple ID. BINGO... that's your old email you were looking for.
4. Go up to the beginning of this blog, to figure out the password.
Okay, I pray and pray and pray this all works for you. I definitely know your pain.