While Canonical still has discussions on whether to set Chromium as the default browser on Ubuntu 13.10 Saucy Salamanader, Chromium 28 has been added to the default repositories of Ubuntu 13.04 Raring Ringtail, Ubuntu 12.10 Quantal Quetzal, Ubuntu 12.04 Precise Pangolin.
Chromium 28 comes with bugfixes, improvements and optimisations, no major new feature added.
So, to install Chromium 28 on Ubuntu 13.04, 12.10, 12.04 and Linux Mint 15, 14, 13, do:
$ sudo apt-get update
$ sudo apt-get install chromium-browser
Bonus: Install Chromium 28 on Mageia 3:
# urpmi.update -a
# urpmi chromium-browser