Same problem here.
I have three accounts on my iPhone. 1 GMail, 1 IMAP and 1 MS Exchange. After I disabled the GMail account the IMAP account showed a negative new-emails badge. ( image:
http://img19.imageshack.us/img19/3136/img0001boy.png )
I tried deleting the account and recreating it on the iPhone, but it didn't help. Also tried to re-enable the GMail account, also didn't help.
After I disabled the GMail account I watched some TED seminars using the TED application, which during one of these video's completely locked up the iPhone. I force-shut down the iPhone, started it back up again (took longer than normal). After the reboot the iPhone was showing erratic behavior (contacts would quit when pushing certain buttons, etc).
A few reboots later the erratic behaviour was gone, but I instead was left with the -2 email badge.
Hopefully this elaborate description of the events that took place will help someone locate the problem.
- Robert