you can, but not an OS as we know it. the problem with gui based OS's is that they require hardware to be the mediator ( I.E. the mouse and keyboard ) between the machine and the human. The problem with hardware is that in order for it to work properly, it must have an address in the system's registry. Even for the computer to recognize the flash drive it has to pass through the usb host controller which must aslo have an entry in the registry. Hardware Bus controllers are programmed to reference this registry on the same storage volume as the OS, i.e. the hard-disk. So, in order to have, say Windows, on a flash drive and have it work, the registry file would have to have an entry for every possible hardware combination. Now it can be done, anything can. For instance, you could write your own executable file on a floppy, boot from floppy, and have the cpu write its hardware entries. But for the average person, fuck it. If you want an OS on a flash drive, use a text based system such as linux, DOS, or hell, write your own shell code.
Curious, why would you want to do this?? If you want to steal a password or files, all you need is an IP and telnet.