Acronym for Random Access Memory. Duh.

You can do a fairly bare install of a modern Linux distribution with 16mb of memory, although many installers require more memory, once the OS is installed, you should be fine.

32mb of memory can be a reasonably useful Linux install if you don't have X(1) or any other memory hungry programs running. 32mb of memory would make a reasonable non-caching firewall for instance.

64mb of memory is where a machine starts becoming usable interactively with X(1), but don't run mozilla :)

128mb is a reasonable amount of memory for a Linux install, but if you want to run mozilla, and other memory hungry programs you probably need:

256mb or 512mb. 512mb is a nice amount of memory. I have 512mb on my desktop, which is also a fileserver and runs the Wiki.

1gb of memory is just getting silly :)