Assuming buying more memory is out of the question there are many things you can do to tighten up memory usage in Linux.
Many Linux distributions out of the box are quite bloated from a memory perspective. They run more services and offer more features than most of us will ever need. By removing many of these services you can free up several megabytes of real memory.
My own system is a 486DX2-66 with 12MB of physical memory and 12MB of swap space. It has run Linux for the last 3 years quite happily, and hopefully it will run Linux for several more years. :)