How small do you want? Floppinux fits on a floppy disk.
Tiny Core's largest image will almost certainly fit on the smallest capacity USB thumb drive you own*.
Puppy Linux has a diverse ecosystem that pulls from other popular distros and their images generally run to around a gigabyte.
* It's less than 256MB. There are a few reasons you might have a smaller drive than this, but for most people this is true.
