BuddyPress.org

In our case, it turned out to be a permalinks issue. The registration form would be submitted, but not directed to the right script. Make sure your .htaccess file is writeable, the resave your Permalink settings.

@mercime Registration works normally in WordPress, as well as on a clean staging site with all the same plugins.

I have also had this problem, on http://persephonemagazine.com/register. No fix yet, but we are trying to track it down.