Aside from a direct serial connection, a Palm on a network can also act as a Telnet client, and log into servers remotely. Due to security considerations this may only be useful on a LAN, but it's still a very handy option to have at times.
For more secure connections, Palms can use the SSH protocol (both version 1 and version 2). This is great for remotely operating a server over the Internet, from whereever you happen to be.
To network a Palm to a Linux machine, these instructions may be helpful.