Redmine

On each issue page, provide a play/pause and stop button to automatically log time so you don't even have to think about it.

1. Dev is assigned an issue to work on
2. Dev opens issue page
3. Dev presses "play" button to signify start of timer
4. Dev gets called away to a quick meeting, presses "pause" button
5. Dev resumes work, presses play again
6. Dev finishes on the ticket for the day and moves onto other work, presses stop button
7. Popup dialogue appears for comment
8. The time is automatically calculated from the duration the play button was active
9. Time log is updated with above info

Not 100% sure whether you need the "pause" button, it could just be logged as separate blocks of time.

Maybe more suited to a plugin?