If the BIOS allows you to specify a USB device as boot device, you probably can boot off a USB stick, provided that the stick contains a bootable system, like raggerund and uncle_philip pointed. Though I'm not sure how many actual Linux installers (for "regular desktop operating systems") you'll find..
But there's another possibility. Many Linux systems, such as Slackware (most recent version as of now is 12.1), allow you to install the system over network connection. Therefore you could, for example, boot the system off a diskette (set) and tell the installer to fetch the actual files from someplace over the network; I'm not sure if Slackware offers a USB stick installer, but it seems it's handy so you might want to check it out.
There are also usb-connected optical drives available, so if you can't figure anything else out, see if you can get one of those - loan, if you want.