Open-source and commercial 'with-sources' Help Desk apps
First off: why would you need sources?
Sometimes a company would like to modify a helpdesk application to fit its needs, to integrate with existing automation systems, internal websites and user-databases, document warehouses etc. That's when 'open-source' or commercial apps (the 'sources included' ones) fit well.
Open source vs. Commercial
Let's not start a holy war here, but still we should point out some obvious pros & cons for both. Open-source's best advantage is that it's free. That's about it. You're on your own dealing with maintenance, upgrades, technical glitches etc. Also there's a risk of the software being abandoned by its contributors... But, well, it's still free. This beats everything else.
osTicket (open source)
osTicket has a pretty standard feature set. Comes with Knowledge-base, file-attachments, web-based UI (like nearly all the apps reviewed on this website, we should probably stop mentioning this), Email-integration... It has no automation rules, no asset-management and pretty outdated UI, but it seems to be the most actively supported systems today. The tool uses PHP and MySQL.
HelpSpot is a commercial system for hosting "on-premises" but since it's PHP-based, you actually have the source codes at hand. But the source codes are not offered "officially" so they offer no support if you decide to modify the code. The feature is also pretty standard, this helpdesk has everything you need, including a Knowledge-base, ticket-management, email and even automation macros. No social integration though.
Jitbit Helpdesk is proprietary, but it has a "sources-included" license. The company even offers you a svn-access (actually, it's mercurial-access) to the customers on the top plan, so you actually can see their latest commits even before they release something. As for the feature set - this helpdesk has everything you might need. The only feature they miss is Twitter-integration, the only downside we found - is that it's based on Windows-platform (some would call this an advantage, though).
Brimir is a new kid on the block. It's a very very basic email-helpdesk system written in Ruby-on-Rails, but it does the job. They also offer a hosting option for $19 a month for 5 agents.
Omni Help Desk is a pretty outdated PHP-based solution that looks currently unsupported. But we still included it into the review due to its popularity in the past. The system is actually pretty usable, even thought it's pretty basic: you get a ticket-creation web-form, email integration, attachments and a sortable/filterable ticket queue.