What are some alternatives?
When comparing ZenDesk and Bugzilla, you can also consider the following products
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
Jira - The #1 software development tool used by agile teams. Jira Software is built for every member of your software team to plan, track, and release great software.
LiveAgent - LiveAgent is a fully-featured web-based live chat and helpdesk software. It harnesses the power of a universal inbox, real-time live chat, built-in call center, and a robust customer service portal. Start you free 14-day trial today.
Redmine - Flexible project management web application
HelpScout - Help Scout is a simple, straightforward way to provide excellent support
Trello - Infinitely flexible. Incredibly easy to use. Great mobile apps. It's free. Trello keeps track of everything, from the big picture to the minute details.