Go to settings and tick the box that says "Protect your tweets"
Only if they go on your profile and notice that the message option isn't available anymore.
Go to their profile and click "unfollow"
Go to the persons profile and click on the "unfollow" button. If you want to stop the person being able to view your profile then you can also click the "block" button.
Don't sign up for it or do not go on it again
You can block Aaron Carter on Twitter to stop him from following you.
He was asked by WWE officials to stop using Twitter. This was most likely as he was blocking many people for asking simple questions.
You could tell them to stop. Or you could report it to Twitter
Don't tell people. Don't list them on your profile.
Revoke the applications access on Twitter.
They don't allow it but they can't stop someone from making an account in that name. They have introduced the feature of "verified accounts" so that celebrities can verify their account to let their fans know that is their real account. If you find a fake profile, you can report it to Twitter and they will remove it. Just remember that they will have a lot of requests like this and it may take them a while to actually remove it from the site.
Stop tweeting
Go to your account settings on Twitter and then the applications tab. Revoke the access so that MySpace will stop connecting to your account.