Intercom has created a great solution that enables companies to better interact with their customers directly from your product—through a dashboard, integrated email and more. That stuff matters a lot to us because it adds value to the quality of support that we can provide. They have a great app, although their internal messaging isn’t great.
JIRA is a begrudging choice because the tool has so many drawbacks: It’s overly complex, slow, has confusing terminology, and mind-boggling frustrating design choices. But when wielded effectively, its level of customizability allows you to simplify the screens and customize the workflow for each team to make the tool match the process. This is the greatest aim of any project organization tool. We integrate JIRA with Github, Zendesk and Slack, so that tickets are our universal increments of development.
We use Trello for product backlog. We like to keep that separate until items are ready to be spec'ed, broken down, and queued for development. Trello is great for this because it allows us to easily move around ideas that aren't yet ready for development. When they're ready, they are assigned user stories in the appropriate boards in JIRA.