http://www.vbulletin.org/forum/showthread.php?t=184449

This vBulletin product / cronjob bans inactive users at regular intervals:

• users who have registered but haven't confirmed their email within the past 21 days and never have posted (applies to user group 3 only)
• users who have registered but haven't connected within the past 90 days and never have posted (applies to user group 2 only)

There are no user interfaces or settings, but you may change the cronjob interval from the AdminCP - Scheduled Tasks.
A short installation guide is included.