We use sightmax - it's OK, but a little buggy. The real advantage is it is a one-time fee instead of a monthly recurring fee.
Although not free, we use http://www.livesupport.com, it's much cheaper then liveperson, and has same functionality.
You can also try olark and zopim. Both offer free website chat at the moment just like livezilla. But I think livezilla is the most widely known open source project for live website chat and support.
Hi, I have got two free live chat software for you which i have already used. http://mibew.org/ ( live use at Hosting Basket ) http://www.craftysyntax.com I hope this will help you.
LiveZilla is just amazing! I am using livezilla myself . If you need any help in installation contact me . helponchat.com
Another vote for LiveZilla Live Help. I am using it for 6 months now on 3 websites and don't miss kayako at all (far from it).
If it is for personnel website or less traffic website then you can think about free live chat softwares.
I'm another fan of livezilla. Seriously it's really powerful, and so useful. Take a look at it. I've never had any issues with livezilla