However, I forgot my Apple ID password. So, I clicked on the Reset Password link.
Just over four hours later, I received the promised E-mail in my inbox. Here's a quote from this E-mail:
"Please note that this link will expire 3 hours from the time it was sent."
How useful! Offer to reset a customer's password, but don't send the mail until an hour after it expires. Yay.
Update: As Chris points out below, the problem isn't Apple's, but Yahoo's.