Ask HN: How to handle “backlog overflow” from user feedback and feature ideas?

While developing a product (or side project), we accumulate a big amount of user feedback. We use Trello right now for tracking and managing the development. But it's terrible for keeping user feedback, feature ideas, bug reports, etc.

As a developer, the original user feedback or "user story" is often extremely useful. It helps to understand the real problem and implement the most efficient bugfix. Same for feature requests, which are just problem descriptions explained as features.

How do you capture and manage inputs for your project, so nothing slips through the cracks?