Tyler: There are several of them! Puppy Linux is 'marketed' as a stripped-down version especially for older PCs. It's only 100mb! You can run it off an older thumb drive! Lubuntu is 'Lightweight Ubuntu', meant for older PCs. There's also something called Linux Lite (never saw it, only heard of it).
Google 'Linux older PC' and you'll see lots of articles for distros. Rehabilitating older PCs is one of the main things Linux is used for!
Some actual machine specs? Ram and CPU?
Assuming it's an old P4 with 1 gb of RAM for example.
Lubuntu will run happily on that.
any old linux live will probably be fine. susie or ubuntu being the most likely candidates.
Any distribution that uses LXDE will do fine.
Xubuntu is also a good option.