FreeOrion numbered releases are available for download for various Windows versions, OSX 10.6+, and various Linux distributions:
Both numbered releases (eg. 0.4.1) and more frequently-updated test builds are available. Numbered releases are probably more reliable and less likely to have major bugs, but may be significantly out of date compared to the latest developments in the test builds.
Please note that FreeOrion requires OpenGL 2.1 or later. With OpenGL less than 2.1, there may be poor performance or crashes.