For the Raspberry Pi (version 1 and 2) there are multiple operating systems available. Downloads of each operating system can be found at www.raspberrypi.org/downloads/
Raspbian is the preffered Raspberry Pi operating system and mostly used by others. It`s based on Debian and features official firmware and tools.
I recommend Raspbian
Snappy Ubuntu Core
Snappy Ubuntu Core is a relatively new operating system. It`s based on Ubuntu Linux but with extra features. This might be the next big thing!
OpenElec is the prefferd operating system when you want to turn your raspberry pi in a HTPC with XMBC software.
Pidora is Fedora Linux for the Raspberry Pi. It`s a bit different from Raspbian and really interesting if you are familiar with Fedora/Red Hat Linux.
RISC OS is unlike the other distributions. More information about RISC OS for the Raspberry Pi. I have no idea why you would run this operating system.
Ubuntu Mate is out now