Is there a way run Emacs from a USB drive? I am a Windows user and I would like to be able use it on any PC without an Emacs install.
Yes, the "normal" Emacs distribution for Windows is precompiled and just runs without having to do any install. Just get one of the *.zip files from the usual place, unpack it onto a USB disk, and you can use it directly. (The actual binary is inside the "bin/" directory.)
The only thing you may want to do is set it up to look for ".emacs" always on the USB disk instead of on your hard drive; see
(info "(emacs) Windows HOME")
on how to do that.