When you are changing your password, you do not need anything to be sent to you because you are entering a new password right on the Account Settings page and it takes effect immediately. If you are unable to log in with the password you entered, or with your original password, you can use the Lost Password feature to have a new one generated.
If that is what you attempted and still are not receiving any mails, you should take a look at the "Problem: I haven't received my password!" sticky thread in this forum for all of the assistance we can offer for this (particularly the second paragraph regarding spam filters).