Most online accounts include a 'secret' question to assist in password recovery, the correct answer to which is supposed to validate that you really are the legitimate owner of that account. The problem is, the 'secret' question is generally none too secret.
For example, common 'secret' questions often include the name of your favorite pet, the city you were born in, or the high school you attended. Easy information for anyone to gain just through idle conversation or, if you're a Facebook/MySpace social networking junkie, just by doing a simple Google (or Yahoo or Bing) search.
This may be one of the few times that it really is okay to lie. Instead of giving the correct response to the secret question, make up a bogus answer that you can easily remember but which cannot be tied back to you through conversation or search engines. Say your high school was West Central High. Instead of using that as the answer to "Where did you go to high school?", enter a fictitious and nonsensical passphrase instead.
Of course, this also assumes you have used a unique and strong password to begin with. And if the password recovery/reset function is delivered through email, that the email account you have specified is an active account that you routinely monitor.