As a small-scale software developer, I need to track bugs and feature requests. Of course I could write something like this myself, or use something like Bugzilla, but my users probably feel my time is best spent on other things - such as actually fixing the bugs and adding the features. :)
I would love a low-cost option (this is a hobby that costs more than it makes), if possible with these features, in priority from most important at the top:
I know I am probably asking for too much, but it is the web and 2010, so I should feel entitled to other people's work for free or cheap. ;)
We use Trac at work, and it does all the things that you have set out above, with the added bonus of integrating with subversion and other source controls programs.
Have you considered the fogbugz student & startup edition?
ClockingIt seems to be a perfect match.
We use Unfuddle (www.unfuddle.com) and its great. It's rock solid, supports multiple projects, issues a ticket number for every new ticket, allows discussion (via comments and 'notebooks') and has a simple and a clean design. In addition to all this, its only $9 for the smallest paid plan which allows 4 active projects and 10 developers. Their free plan, AFAIK, allows only one active project. They also support subversion and Git hosting. All in all, this has worked out great for us so far. I am not sure about your last concern though.
You could also try Pivotal Tracker (www.pivotaltracker.com) - its completely free and take a very different approach towards issue tracking in general. You may want to check that out as well.
We tested a few open source options a few years ago and settled on redmine (http://www.redmine.org/); we've been very happy with the results.
I also recommend having a look at gforge: http://gforge.org/gf/.
You can have a look to JIRA, it's not Free but very cheap for small number of users (10$ for 10 users)
I would recommend Assembla
I am using it more than 2 years, and fully satisfied.
We use Elementool.com.
Works well and allows us to work with outside vendors easily. Also has plugins for Visual Studio IDE so that tickets and tracking are incorporated into our dev environment.
I would highly recommend Redmine, it's very close to JIRA and free.