Acronym for Random Access Memory.

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.

1GB of memory is just getting silly :)