Really it depends on how old "old" is. If you're talking a machine that's about 500Mhz w/ 92MB of RAM, a GUI-less version of Ubuntu would probably work (and since it seems you're new to linux, Ubuntu is also very friendly to use and install).
If the machine is older than that, then even some of the newer distributions might be too much, going with something small like DSL (which i love because you can burn it to a business card CD or USB drive).
Personally i've been a huge fan of Gentoo for years (back when you'd have to bootstrap the system from nothing). The distro has come a long way and there's a lot of community support. And it's lots of fun to play with.
Depending on what your system can handle and what you think you'd be comfortable with should be the big criteria you should be considering for your choice.
Ubuntu - easy to install, good community support, easy to use
Gentoo - a bit more hands on with installation and configurations, great community support.
DSL - easy use (just boot from a bootable device), great if you want to do something like a disk less system