The best Helpdesk system I've used is CT (see earlier posts from Raj Patel and Rob Butterworth) but this was an in-house system and not available as OSS unfortunately.
Since starting my own IT Support company I tested dozens of systems -- all the time comparing them with CT. The only ones that came close (and fitted my budget) were 'AdventNet ServiceDesk' and 'Kayako eSupport' (http://www.kayako.com).
We went with Kayako as the interface is pretty slick but most of all the email ticketing is excellent and worked as well as the in-house CT system I used to use.
Additional Notes:-
1. Kayako are due to release version 4 shortly but they're keeping tight lipped about the features at the moment.
2. Kayako runs on LAMP
3. They now provide a hosted solution too.
4. It's also very cost effective
5. You can try it free for 30 days
6. We used http://www.supportskins.com to customise the design and integrate it with our website
7. Can be used for internal company use or for support companies like ours providing IT Support to multiple clients.
8. Very customisable
9. Built in Knowledgebase, File downloads, Reporting, CRM (basic)