I have Ubuntu booting off the internal hard drive and Fedora 7 on an
external USB (on a laptop). If you're talking about installing another
Linux distro on a USB drive (or stick) it's a little more involved as
you have to rebuild the boot image to include the appropriate drivers
otherwise it won't recognize the hardware.

To install Ubuntu on an external drive (and hundreds or other Ubuntu
tips and tricks) I can highly recommend Ubuntu Hacks as an excellent
resource (published by O-Reilly and available on Amazon).

If you want to put Fedora on an external drive I can detail how I did
here if anyone is interested.