What is the best linux distribution for an older computer?

Try puppy linux. It will work fine even on a pc with 64 mb or less ram, or else try installing DSL (Damn Small Linux).

I installed puppy Linux on an older machine and am very happy with it. It boots quickly and seems to be very stable. The only drawbacks I found were I had to do a little config file editing to get the Samba server to work, and still need to edit the grub file for a clean boot up. Other than that I would recommend puppy for an older machine Puppy 5.01 reminds me of the old windows 95 with it's look and feel. I use it for a media center and file server on my home network. I have tried DSL Linux but it is just a little too plain for me. I guess if your machine couldn't run puppy then the next choice would be to try DLS Linux.

puppy linux is good. But for the computer you are saying, try to install Mandrake Linux 9 or 10. Now is known as Mandriva. It is fast and safe. Boot , on 10 seconds with InstantOn tool. More info here: http://www2.mandriva.com/

Based on your needs, I will recommend Puppy Linux. It is fast even on computers older than yours.