[open-source] What is the best open source help ticket system?

It absolutely depens on what your goals are. The Bugzilla and Trac systems mentioned are nice but geared towards bug tracking, which is just very different from a tool you'd want to use in a helpdesk-type setup where end users would raise incidents.

If the latter is what you are looking for I'd suggest you take a look at OTRS which is a very capable trouble ticketing system. It also has ITSM extensions, which makes it able to support ITIL processes if you need to.