We are running an Ubuntu 12.04 server with the Aegir hosting system and recently upgraded the server software with apt-get. The next day we noticed that the cron queue wasn't running, so we began to investigate. It turns out that the Drush package for Ubuntu had recently been upgraded to Drush 5.9.1, which is incompatible with Aegir 1.x version.
So, after some searching, we downgraded the drush package by searching the apt-cache for the previous version of Drush.