I\'ve used Trac/Subversion before and really like the integration. My current project is using Mercurial for distributed development and it\'d be nice to be able to track issues
Mantis has a beta integration for Mercurial: blog-post and code.
I'd also like to add Redmine to the list. I started with Trac, but I found the mercurial support (and the administrative interface for everything) to be much better in Redmine.
TracMercurial integrates Trac with Mercurial. Assembla provides free Mercurial hosting with Trac integration.
The idea is that you have a central repository as your master and upload all the subsidiary changes from local repositories into the main one.
I recently developed a Trac plugin that integrates some Mercurial functionality that TracMercurial Plugin doesn't support yet, it's called TracMercurialChangesetPlugin. It allows you to search in your changesets, to have the cache synced, to view a changelog in your related tickets...
You can read about it at http://tumblr.com/x8tg5xbsh
Bugs Everywhere is a distributed bugtracking system that supports Mercurial.
BugTracker.NET now supports Mercurial integration in the same way it supports Subversion and git. BugTracker.NET is a free, open source, ASP.NET bug tracking system.
Other free, open source bug trackers that support Mercurial: