I've read bios of astronauts, and I've noted that many of them majored in physics. So I suppose that this is one way to become an astronaut. Of course, many others took the military route, and became astronauts after flying naval and air force aircraft. I know that fighter pilots are required to have a minimum of a bachelor's degree, but I don't think the military requires a specific field of study.
Anyway, I'm definitely not the person to talk to for advice on this, but this is what I've heard.
Thanks for the reply. Right now I'm trying to decide what to do with my degree, and where to go after I"m done undergrad. I'm basically just taking every little idea I get and running with it to see where it goes. This came up in conversation with a buddy of mine, and I figured, why not learn more, could be fun.
The basic requirements are simple ( http://www.nasajobs.nasa.gov/astronauts/content/broch00.htm#bqr [Broken] ). What actually sets some people apart from others, I don't really know. If/when they decide to go to Mars, or even back to the Moon, I would think that a degree in something like Planetary Science might be useful to get selected. Of course, physics, and other similar degrees too.
With the "3 years of increasing responsibility" requirement, you should probably try to make it as close as possible to the space program. Or, they seem to like sending teachers up, maybe you could do that too ;)
These are all just guesses on my part. I plan on applying too. Perhaps we'll both be stepping onto Mars one day :)