On small LAN networks that do not have an internal DNS server. There is a nice technology called ZeroConf that uses multicast to enable name lookup resolution. It has been baked into OS X for quite some time now. Linux and other UNIX flavors have been picking this up as well. OpenSolaris also includes this but enabling it is not on by default (At least with 2008.11). Here is a quick howto.
Edit the file /etc/nsswitch.conf and make sure that the line that begins with
contains the following
hosts: files dns mdns
Then you should be able to ping any machine that uses Bonjour. For example, if you have a Mac that is named mycoolmac then you should be able to ping mycoolmac.local