We us phplivesupport. We've used Kayako (and still have an owned license for the suite), but don't use it now as there's no Linux support for the chat. We HAVE to run Windows to use their chat support. Not good enough!
We use phplivesupport.com (osiCodes) and have used phplivehelper.com (turnkeywebtools) as they are both browser based. So even if I'm out of the house and at a family member house etc, I can still jump on live help if needed, no software to install. We've used the osiCodes solution for probably 5 years at this point.
As for the free softwares out there - I have looked at them (for clients etc) but I still come back to the paid version. Free can be cheezy sometimes. It's like operating a business site on a free hosting service - you get what you paid for. For $100 (one time fee) and then install the software on your own server, and have full access to customize the code, templates and inner workings of the software - the phplivesupport can hardly be beat.