Just drag this bookmarklet to your bookmark bar. Click it for a 32 character (letters and numbers only) password.
There were a number of solutions out there for this but nothing quite as simple and straightforward as I wanted. If you are looking for a fancy password generator that gives you lots of options, this is not it. If you are looking for a way to click a button and get back 32 random alpha-numeric characters, then this is as easy as it gets.