To support Ticket Tracking, I love and use Trac all the time. For Emails, Bugzilla I think has an outward facing submission form/ bug tracking system that users can report through. Trac does not, but is great for developers b/c it's simple although somewhat hard to setup at first.
Stay away from Trac, it must be confusing or something because there is almost always some problem on trac runs sites, you are better off running wikimedia/bugzilla.
Trac bad example: Yesterday the pkgcore people asked me to file a bug, I went to file but couldn't open a ticket. The dev's were surprised that it hadn't been set up right they thought it was working. I've seen many open source projects that use trac that don't allow me to file bugs, or find what I'm looking for. I usually just leave and ignore the issue. Not exactly appropriate, but how does one file a bug when the bug tracker doesn't work? I know email a dev, mail the list.
These services aren't hosted though, fyi.
http://www.bugzilla.org/
http://trac.edgewall.org/