osTicket - osTicket is a widely-used open source support ticket system.
Zammad - The Zammad - Help Desk and Ticket System - Community Page
Zendesk - Zendesk is a beautiful, lightweight help-desk solution.
Freshdesk - Freshdesk is a cloud-based customer support software that lets you support customers through traditional channels like phone and email, social channels like Facebook and Twitter, and your own branded community
FreeScout - Free open source Zendesk & Help Scout alternative: help desk, shared mailbox, email management...
Request Tracker - open-source enterprise grade issue and ticket tracking system