Sometimes when I received too many emails, I just deleted them all, and counted on that important ones will be resent again.
(I watch all svn/git commits and Moodle boards, so my research and teaching were never affected.)
When people asked why I did not reply their emails, I apologized with the above reason, so that they knew it is not personal.
This appeared to be working fine so far, but follow my strategy at your own risk.
🙂