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

Intercom - Intercom is a customer relationship management and messaging tool for web businesses. Build relationships with users to create loyal customers.

FreeScout - Free open source Zendesk & Help Scout alternative: help desk, shared mailbox, email management...