The core ROS team maintains ROS Hydro packages for Ubuntu 12.04, 12.10 and 13.04 for i386 and x86_64; these packages should work on most Ubuntu variants and BSPs for those architectures. See the Ubuntu installation guide to get started.
I maintain some builds of ROS Hydro packages for Ubuntu 12.04, 12.10 and 13.04 for the armhf architecture, which supports most of the ARM boards currently on the market. Most boards ubuntu variants and BSPs, including Linaro/LUbuntu, work with these debs. The 13.04 builds are the most complete, so if you can find a BSP based on Ubuntu 13.04, that's probably your best bet. Once you have Ubuntu up and running, take a look at the Ubuntu ARM installation guide
Could You be more specific on the board You trying to use? Short googling came up with this wiki.ROS.org [manual](http://wiki.ros.org/IntelGalileo/How%20to%20install%20ROS%20Hydro%20on%20Intel%20Galileo) of installing Ubuntu + BPS + ROS Hydro on Intel Galileo. So, it appears, in general case it's possible :) Still, You should consider using [rosserial](http://wiki.ros.org/rosserial) instead.
This should be a good start. http://wiki.ros.org/hydrohttp://wiki.ros.org/ROS/Installation