Google follows strict policies for Adsense Publishers to follow. If you violate any of those TOS then your account will be banned from Google Adsense. Once they ban your account it very difficult or almost impossible to get your account back in action. Only if you have complete proof that you haven't violated their rules there are a few chances to get your account back. Submit those stats and proof to them for consideration.If google feels that you are correct you might get your account back.
Once they disagree with your proof do not approach them again.According to Google TOS once your account is banned you can never re-apply for your lifetime.
Even if you try to re-apply for an adsense account using different e-mail address you will be caught.Google has an excellent tracking system and you can never cheat them.Even if you re-apply with a new address or web-site you won't be approved.Google check it's banned publisher's database before approving any new accounts.
So never try to cheat the Search King Google.They are the best in tracking and they will find you by any means.
Still there is one way to "Re-Apply for an Adsense Account even if you have been already banned from them.".
Remember Google only bans adsense publisher account and not their web-sites.One legal trick or method to re-apply your adsense account is to use your friends name.
Consider you have a web-site like "www.yourdomainname.com" on which you have used your adsense ads. After your account has been disabled the first thing to do is try convincing google that you have not violated their terms using suitable proof.If this doesn't work then go the other way.
It's time take the help of you friend.Create a blogger account with his google account and apply for adsense program in his name and in his address.Now google will easily approve his account.Then get the permission from your friend to use his adsense publisher id in your website which is "www.yourdomainname.com". Now as per Google TOS you can use your adsense ads on any number sites once your account is approved.So you again make money from adsense.But you will be get the checks in your friend's name.Make sure you have very good understanding with him and so get your percent of income from him.
If your friends has no web-sites then no problems you can get all the money provided you explain everything to him and get his permission.
That's it ! You have successfully re-applied for Adsense Account. Make sure that you don't violate their terms again and get more problems for your friend