Update: Apple restored the password resets on Friday night.
Apple suspended the password-reset functionality for its iCloud and iTunes services following a published report that hackers could exploit it to hijack other people's accounts.
The password reset page stopped loading a few hours after The Verge reported there was an online tutorial that provided detailed instructions for taking unauthorized control of Apple accounts. The report didn't identify the website or the precise technique, except to say it involved "pasting in a modified URL while answering the DOB security question on Apple's iForgot page."