I have just submitted my very first public Joomla extension which was requested by Renzki and also something that I would need for other projects. It is MysqlAuth and information about it can be found at the Joomla extension repository
This extension has a component and a module which allow joomla to share, and synchronize, users with another site. The idea is from the drupal mysqlauth. So if you have already with another site (mysql based) then you can install joomla in another place and have the users of that other site listed as joomla users.
What I mean by synchronization is that if your users change their password, from your official site, they will still be recognized in your Joomla site.
What is required is that you should not allow registration with joomla. All password reminder links also should be redirected to where your users are stored, not with joomla.