As America is not only the greatest nation in the world, but saved us from the terrors of Nazism, Americans don't need a visa in Germany (to be honest, it has nothing to do with Nazis, i just like this tangent. Basically, if you're from a rich non-EU state, you don't need a visa). If you come to Germany to study all you'll have to do is register with the authorities within two weeks (like even Germans have to do when moving) and apply for a student's residency permit within three months.... In other EU countries the rules most likely differ cause we like to keep things complicated in the EU...
There's a catch, though: As an American friend of mine (he's doing some weird stuff with particles, colliders and space dust) just found out, the
ESA will not employ non-EU citizens as their work still counts as defense-related. So that's a line of work that won't be open for you.
EDIT: He's working on something called
HESS - maybe you can make some sense of that, LP. I surely can't.