OOZ is an open source helpdesk and ticketing system.

It does not use a template system for the user interface which is a real pain- you have to dig into the php code to make template changes.

Recommended for intermediate and advanced users. 

OSTicket is an open source helpdesk/ticket system. It allows anyone to submit a ticket using an online form.

It is very basic in functionality but for a simple solution is useful. 

Trellis Desk is a powerful, robust help desk solution for your business.

The templating is similar to IP.Board and vBulletin, they also have a few
templates for sale. It is pretty simple to change the logo graphic to your
own name Installation/upgrade seems to be pretty simple.

It is a free system that seems to be as good as kayako for smaller sites it is an all round good performer. Has second level support, ie agents handle most requests but can escalate the request to level II support.

Even better, it's completely free; you don't have to pay any license fees to use Trellis Desk.

 *Review posted by a member.