Linux is certainly the most used and best known operating system that can be used with old computers. It is, however, not the only one. Some of its alternatives are mainstream operating systems, some of them are mainly designed for academic purposes, some of them are geeky projects of open source developers.
If you would like to resurrect a computer from the Dark Ages, let us say a 386 or a 486, or an early Pentium, you might try some of the floppy-based distributions. It would at least be an interesting experiment. Another possibility would be to install Minix on the computer. That is what Linux Thorvalds did before he had written a working kernel for something that would be called Linux.
Minix is POSIX compatible Unix-like system. It can be installed on a computer with 8 MB of RAM. Originally it was meant to be an educational system, but since Minix3 it has been designed to be used in embedded systems and low end computers, e.g. by "One laptop per child" project.
It is a very compact system, and a full install of Minix can be done in around 50 MB hard disk space. Consequently it also boots in a few seconds: you don't have to wait for minutes before your system is up and running.
Minix is not as mature operating system as Linux is. There is only a limited selection of software available for Minix, but the selection includes most of the important Unix tools. In fact, the list of ported software is pretty impressive for an educational operating system. Thus it is great choice for learning Unix or programming - you can basically install it on any old PC you still have in your garage.
If you are interested in Minix, you should read the interview of Andrew Tanenbaum, its creator, in Free Software Magazine (2007).