I want a Linux OS that I can load on a flash drive, but I don't want to relearn an entire operating system. I want to know which tiny Linux installations are most like Ubuntu. For example, I'd like to use the apt-get package manager, the Gedit text editor, and the bash shell. I'd like to use something that's already popular, stable, and highly compatible, but it needs to fit comfortably in one gig of my four-gig flash drive (just the essentials; I'll use the remaining three gigs to store installed programs and files). I have no preference for window managers; I just want something small and fast that works like Ubuntu.

What is the most popular Ubuntu-like OS that can be easily run on a thumb drive?

Edit: I'm not sure I understand how this works. I don't to use a USB drive as a LiveCD; I want to plug in a USB stick and use the computer as if it was my own. In other words, I want to be able to install programs on the drive on one computer and use them on another. Do any of these OSs let me do that? Please forgive my ignorance.