The current stable release series is Rhythmbox 0.12.x. The stable release series only receives bug fixes and translation updates, so it should always be safe to upgrade to a newer 0.12.x version.
There are no official binary packages of Rhythmbox. Supporting binary versions for many different operating systems is too difficult, so we don't even try. However several users have created binary packages, and they are available from many sites on the Internet.
There is currently no development release series.