Here's a summary of what I have tried without success:
+Restored phone (iPhone 4s) and configured as "new phone," manually entering settings
+Replaced phone
+Replaced SIM card
+Emptied "deleted items" via webmail interface
+Updated to iOS 5.0.1
+Restored phone, manually entering mail (POP3) settings, without synching any settings, contacts, media, apps, etc. and without enabling iCloud
+Disabled SSL, entered alternative settings for the incoming & outgoing mail servers and the ports
+Took it to Genius Bar 4 times, four different genii (genius baristas/bartenders?) were stumped but one said she was writing a letter to Apple's corporate HQ on my behalf to alert them to the bug. Fortunately, it crashed while she was experimenting with it so she saw how frequently it happens, which is very frequently.
Since it crashes when all I've entered is my Apple ID and my POP3 settings, I think it must be related to how it connects to my hosting company's servers. My hosting company is "The Small Business Authority" (thesba.com) formerly known as Crystaltech. I can't help but wonder if other customers of this company are having similar problems. I may have to change hosting companies--not the end of the world, but shouldn't be necessary. My iPad 2 with iOS4 still works great, as does my iPhone 3G, with the exact same settings.
It also seems like it might not crash when I'm connected to WiFi, but maybe that's just my impression because I'm so rarely on WiFi that I haven't noticed it happening in those rare instances.
My phone screen also kind of flickers (or more accurately, the image shakes very quickly up and down) sometimes when downloading attachments. Not sure if that's related, but seems like it might be.