A Linux port exists (at least an apparently working kernel).
This port, called PSXLinux or Runix, is based on uCLinux due to the fact that the original PlayStation has no MMU.
The Runix website has apparently been relaunched in November 2008 but as of April 2009 there is no information whatsoever available.
Also the original download page is not available. Fortunately Giuseppe Gatta made the files available, see link below.
Probably we will also put these files for download in the near future. We are currently playing with it on our PlayStation.