Bad Method:  Break your keyboard and chuck your computer out the window. If you're banned by one website it's the exact same thing as being banned from EVERY website and there's nothing left to do but give up on the Internet altogether.

Good Method: Walk away from the keyboard, grab a snack out of the fridge and give some thought to what happened and how you might avoid it in the future. For some this might take a few minutes for others it might take a few weeks. Luckily, the Internet is a huge place and there are other websites to go to and try not to be banned from.

Bad Method: Refuse to go away. Learn about proxies and other methods to keep harassing the website who dared ban you. Surely if you continue to bug them, they'll let you back in! It's your right to be able to create 100 different Yahoo email accounts, right? You'll show them!

Good Method: If you've been told to go away from a website, you might try privately emailing the site owner or a moderator to see about your chances for getting involved with the community again. Chances are, though, if it's come to this, you have to face facts and move on, finding another community online with similar interests. Remember, though, to not be bitter and vindictive talking down about the site that banned you on the new site you find as people will be watching your behavior and you may end up just getting banned again.

Bad Method: Begin a campaign to let everyone know that website X, Y or Z is horrible and banned you for no reason. And that they're a bunch of big stupid heads and boring and so on and so forth. For one, no one will probably care. Second of all, you'll being attention to yourself as a potential troublemaker and may end up getting banned again.

Good Method: Learn from your mistakes and move on. Try not to hold any resentment against the website that banned you. The reasons may not be evident to you right away, but if you let a little time pass and learn from the experience, you may end up invited back to the site someday.

Bad Method: Take it to the real world. Try to do some Internet detective work (snooping!) to take the fight to the real world and make them pay for banning you.

Good Method: Remember that the Internet is a virtual world but that it's inhabited by real people with real emotions. If you've gotten banned, think about the behavior that got you banned is something you would do in front of your boss or your grandmother or creepy Charlie at the downtown pub.
Hopefully these tips will help you learn how to properly handle being banned from a forum or other website. No one likes a sore loser. Or a sore winner for that matter.  If you're ever banned, remember to think about two possible actions you could take and choose the right path.