Install a Linux Operating From A USB Flash Drive
or
Boot from one or more Linux Live CD's on a USB Flash Drive

There are several that allow for this. They allow you to choose 1 or more Linux operating systems on the flash drive.
For this most folks use the "Live CD's" of the distro.
I've listed the information from some specific distros for your reference.

Official Pages

openSUSE
If you know of one that works give me a shout.
See openSUSE SDB:Live USB stick.
"This page explains how to create a bootable USB stick from a LiveCD, or in other words a LiveUSB."

Ubuntu (and derivatives)
See Ubuntu InstallationFromUSBStick.

Fedora
See Fedora How to create and use Live USB.

Linux Bootable Live USB
If you simply want a fully featured Live bootable flash drive with Linux I highly suggest you use Linux Mint.
AFAIK it is the only distro that has everything you need for a fully functional desktop, codec and plug in wise.
Advanced users with specific needs might want to check out SUSE Studio.

Linux Bootable Live USB - Just One Distro

Unetbootin is the traditional program most folks use for this.
It runs from Windows, Linux, and Mac.
It does all the popular distros without issue (except openSUSE).


New on the scene is LiveUSB Install.
It runs from Windows and Linux.
Outside of the official openSUSE tool it is the only program I've found that works with openSUSE.
It officially supports, well



Linux Bootable Live USB - Multiple Distros

For this YUMI is probably the easiest to use though the tools in the next section can also create your multiboot flash drive.
(again, except for openSUSE in my attempts)

 

Next > Page 5 - Utility And Rescue Bootable USB Flash Drive

 Article Index - Ditch Those CD's! A Guide To Using USB Flash Drives
Page 1 - Article Intro, Flash Drive Booting, Advanced USB Drive Formatting
Page 2 - Install Windows 7 or Windows Vista From A USB Flash Drive
Page 3 - Install Windows XP From A USB Flash Drive
Page 4 - Install a Linux Operating From A USB Flash Drive
              or
              Boot from one or more Linux Live CD's on a USB Flash Drive
Page 5 - Utility And Rescue Bootable USB Flash Drive
Page 6 - Portable Apps And USB Flash Drive PC Toolbox
Page 7 - What I Use & Other USB Info