E-mails sent from a web interface could have as much structure as you'd like.
So one avenue would be to set up a nice interface for bug reporting, that just
delivered the form data in e-mail format to the proposed bug-receiving mail list.
Also, if an e-mail receiver (something automated) gave a quick response on missing fields, I think
you could quickly train users (even first-time bug submitters) to provide required
data, even if they're sending from a free-form e-mail client.
Just my 2 cents.
-- Tim