Almost every common disto can run on a usb flash drive. You have a number of ways too.
www.pendrivelinux.com is a good place to start for live installs. Since they are in compressed files, live cd/dvd type tend to save a bit of space.
You can also do real installs to the usb just as if were a real hard drive. (it is to the OS).
You may also be able to run qemu on a few OS's but the laptop would need to be pretty fast.
Don't forget portableapps.com for usb software.