yes. they are called portable applactions that do not need the windows registry to install. they can be found here http://portableapps.com/ . Also some apps by design are stand alone making them naturaly usable on usb.
you can install OS'es on usb flash drives. For some linux's here http://pendrivelinux.com/. You can get windows on a usb flash drive by some thing called BartPE. how to do it and its legality I do not know.
There are 'portable' versions of many programs... versions that can be ran off of a flash drive without having to install anything on the computer itself.