My Hampton Bay ceiling fan has worked well for 10 years. But now the motor hums and the blades won't turn. This is true for all 3 speeds.

Sounds like the motors on its way out to me. Does it do this in forward as well as reverse.
Maybe some others will have better ideas but to me it sounds like its time for replacement.

Do the blades turn freely by hand?

General ceiling fan troubleshooting and help FAQ- Ceiling Fans N More (http://www.ceiling-fans-n-more.com/ceiling-fan-general-troubleshooting-and-FAQ.php)