UPDATED JANUARY 2017: Rename OpenERP to Odoo, update based on new runbot format, add note about OCA
The Odoo Runbot (or simply runbot) is a server hosting installed editions/branches of Odoo.
It is available at http://runbot.odoo.com and is a constantly up to date server running Odoo for testing and demo purposes.
Several of the latest builds of the Odoo branches (7.0, 8.0, 9.0, 10.0, saas and master) as well as development and testing branches are available.
You log in with admin/admin.
There are generally two databases available 'all' (every module installed with demo data) and 'base' (no modules installed).
The home page of runbot shows green (thumb up) and red (thumb down) highlighted squares to indicate a build works (green) or doesn't work (red).
If you are having a problem with your Odoo installation, you can check if the same problem occurs on runbot (in which case it is probably a bug) or doesn't occur (in which case it is probably a configuration problem).
You can also use runbot to see what is different about a newer build than the one you have installed.
Bear in mind this is a multi-user environment. You may see evidence of others using the system at the same time you are using it.
For Odoo Partners, runbot is a platform where you can test the branches pushed on GitHub.
EDIT: (To address question about Continuous Integration)
Hover over any branch with a RED square (thumb down), and you will see a gear icon. Click it and select "Logs". You will then be able to see a detailed logfile indicating what failed.
Several logs indicating what happened during the build attempt will be available:
start with test-all.txt
Note: The Odoo Community Association has their own runbot server at https://runbot.odoo-community.org/runbot