Free hosting of Mercurial repositories
Here are some places that provide free Mercurial hosting:
[http://alioth.debian.org/ Alioth] (Debian's GForge instance) [http://wiki.debian.org/Alioth/Hg supports Mercurial] and the repositories are accessible via [http://hg.debian.org/ hgweb].
[http://sharesource.org ShareSource.org] - A Sourceforge-like server for hosting projects. Supports Mercurial out of the box
MercurialOnSourceforge explains how to host your repositories on sourceforge.
[http://www.assembla.com Assembla], [http://vitaliel.blogspot.com/2007/10/free-mercurial-hostings-for-openprivate.html How to setup + screencast]
[http://mercurial.intuxication.org Intuxication]: free Mercurial hosting (in French).
[http://freehg.org/ freeHg] - simple postmodern developer-centric hosting (HowToSetupFreeHg)
[http://sshcontrol.com/ SSHControl.com] - Free hosting for Mercurial, Git, and Subversion over SSH. Also two paid levels at $4.75/mo and $9.75/mo.
[http://developer.berlios.de/ BerliOS Developer] [https://developer.berlios.de/docman/display_doc.php?docid=1806&group_id=2 supports Mercurial] and the repositories are accessible via [http://hg.berlios.de/repos/ hgweb].
[http://savannah.gnu.org Savannah], the software forge for people committed to [http://www.gnu.org/philosophy/free-sw.html Free Software], [http://savannah.gnu.org/maintenance/UsingHg supports Mercurial] and the repositories are accessible via [http://hg.savannah.gnu.org/hgweb hgweb].
[http://www.bitbucket.org Bitbucket] Github-like hosting service for Mercurial.
[http://www.mozdev.org/drupal/wiki/MozdevMercurial Mozdev] provides free project hosting for Mozilla applications and extensions.
It is planned to offer free hosting on hgserve.org.
Also see ServerInstall and PublishingRepositories if you want to host your own repositories.