A badge for consistently staying below a certain threshold of emails
There could be a few rewards based on time and number of emails. For example a lame badge could be awarded for staying under 100 conversations for a week. But a great badge could be earned for having less than 10 conversations at all time for a full 3 months.
I don't know about this one... some of us correspond with more than ten people at a time. Not checking my email while I'm asleep shouldn't disqualify me from earning any of the badges.