While the dreamcast doesn't have a hard disk to record Linux on or to "swap", it does have enough RAM to support a stripped down kernal, and a CD-ROM drive to handle a Filesystem.
At this time, a CD image has been made available that includes the kernal and some packages including X. This is enough to allow for NFS mounting from a remote server, and keyboard/mouse/display handling for remoted applications.
See http://www.m17n.org/linux-sh/dreamcast for more information. You can find screen shots as an existance proof...
Look at www.boob.co.uk for additional info on the distro...