Distributions
Linux systems come in many flavours: many distributions exist, a few of them can run on PA-RISC hardware.
Available Distributions
The two main PA-RISC Linux distributions are Debian and Gentoo.
As of 2011-07-07 the hppa was dropped from the Debian "Squeeze" distribution, but is in the process of being moved to Debian Ports. Please see the Debian_Ports page for more information.
People have worked on ports of Conectiva, Fedora and SUSE, but they have never been released.
ROCK Linux claims to run on hppa, but it's not very obvious from their website anyway.
Last but not least, there is a port effort of Ubuntu to hppa underway in the community.
Problems
Some distributions have trouble working nicely on the PA-RISC platform. People willing to help improving the situation may take a look at DebianIssues to see what problems are currently being reported there.