Can't guarantee the quality of any third party extensions, but there seems to be one here:
If you have the coding knowledge to write your own plugin, then the information you need is in the
__users table of your database.
The date a user registered will be in
registerDate field and if they have never activated their account, the
activation field will be populated and the
lastvisitdate will be
0000-00-00 00:00:00. From this you could write a database query to generate a list of users to delete.
Ideally you should delete them using JUser's delete function, so that it caputures any related data, though viewing that function at libraries\joomla\table\user.php shows you what needs to be done to clean up the database.
I'd probably then pop the script in a plugin that is fired
onUserBeforeSave, so that it tidies itself whenever someone creates or updates an account (this event seems the most appropriate), though you could use Cron if it needs to be more regular than that.
(I assume you know, but if you want to do it manually, it is possible to use the filters at the top of the user manager to find these users.)