Unfortunately I was on the receiving end of this bug before finding out that it existed. Apologies to anyone trying to download my extensions - I have just enabled all new user accounts.
Updating to Joomla 3.2 introduces a new option which allows you to disable email sending globally. You can find it in Global Configuration in the server tab under the mail setting options.
For this setting to work it writes a new line in the sites configuration.php file with the following:
public $mailonline = '1';
If the line is not present then it defaults to 0 which effectively disables the sites mailing ability.
To fix this problem you just need to go in to Global Configuration and re-save the settings. The configuration.php file will then get re-written with the correct settings and the site will be able to send emails again.
The fix has been made on github, so should appear in the next official release.