AccountKiller
Be logged in on the site. Top right: hold the mouse pointer over your name. In the popup menu, click Account Settings. Scroll down and click 'Delete my account'. Easy come, easy go!
Publicly visible text/images often aren't properly deleted even when you succeed in deleting an account. Try editing or deleting them manually before deleting the account itself. If you're unsure what happens to your tracks: this can be found mostly in the Terms of Service/Privacy Policy; otherwise you can always contact MyHeritage and ask personally. By the way, deletion requests don't necessarily mean your data will actually be deleted (e.g. due to legal obligations).
If you signed up for MyHeritage using a third-party login such as Facebook or Twitter, you probably want to revoke all access from MyHeritage. Click the icon below to find out how.