I was wondering which reports and graphs are actually used by software testing teams.
There are no must-haves. I would like to update your question to "What are useful..." if you wouldn't mind.
Useful reports and graphs would include statistics on:
- Number and type of test cases (features, bugs, etc.)
- Average time spend in the various statuses
- Overall velocity of time from test story initiation to completion
- Who's worked on what over time
- Planned vs actual for work done
Another good chart is https://en.wikipedia.org/wiki/Burn_down_chart which gives obvious visual clue if project is on track.
I like addition which adds all unplanned but needed work at the bottom, to show how addition are delaying the release.