My experience? I receive them and file them under "virus". I guess I have a pretty large collection, heh.
If I have any doubt about whether something's a virus, I forward the email to my university account; the virus screen there catches it (and gives the virus name) if it's a recognized infection.
The SirCam virus/worm sent me a lot of private documents, copied off hard drives, but I have not read them.
I should say that I read mail in Pine on a Unix box, so I'm not subject to these (mostly) MS-Outlook transmitted diseases.
As to the flood of BadTrans mail, I have decided to be somewhat responsible and send a boilerplate reply to each one alerting the user to the infection and pointing to Symantec's page on this virus:
http://securityresponse.symantec.com/avcenter/venc/data/w32.badtrans.b@mm.html
Note that the virus inserts a leading underscore in the email address, so to reply, you have to remove the underscore. (I suspect the virus author did this so that users wouldn't be alerted to the infection by bounced emails.)
In October 2001, my site got a bit over 1.5 million hits (about a million page views), so there are a lot of systems out there with stuff from my site sitting in browser caches for viruses to find. I guess it would be worse yet if I hadn't taken my email address out of the page footer (it used to be on EVERY page).