Look at http://www.handhelds.org/ for some very interesting information and pictures about a ~full~ blown Linux handheld running X!
According to this slashdot article
http://slashdot.org/articles/00/04/25/1325250.shtml
Palm will be using an ARM processor in some future Palm handhelds. I believe there is a port of linux to ARM (http://www.armlinux.org). Before we get started we should plan on developing this Palm Linux Environment so that it will work on any platform: 68k, ARM, what else? The biggest problem for different architectures and different base OS's is the boot loader I think.