Top 3 free Help Desk systems
Hesk is a free PHP based "on-premise" ticket system. Comes with all features a help desk app requires: email integration, file-attachments, web-based UI and others.
The free version comes with a non-removable "powered by" label, to remove it - you have to buy a license for $40. The company also offers helpdesk hosting for $20 a month
Free Kayako - if you're a registered charity or an open-source project, you can apply for a free Kayako license (downloadable version only). Kayako is the oldest and most used help desk software on the planet, used by lots of companies. If you ever had an online chat with Electronic Arts staff (I bet you did) - you've seen the client side of it.
Another free ticket system - Best Practical's "Request tracker" - is written in Perl and runs on any *nix-based system. Again, it has all the basic features you'd expect from a helpdesk. But it also comes with mobile-optimized UI that looks nice on Android devices and iPhones
The system is free, but has kinda complicated installation procedure. However, the company offers installation assistance for about $2500.