I would say the majority of people involved in nanotech are either Chemistry, Electrical Engineering or Physics majors. Here's a breakdown
Chemistry: Understand fabrication process and how to actually make nanostructures
Electrical Engineering: Designing nanodevices
Physics: Understand the quantum physics behind nanotechnology
It is an extremely multidisciplinary field (like robotics), so learning to work with other people is crucial. Chemistry majors are useful in just about any nanotechnology field, though so that might be a good major to start out with while you feel around.
Rice University has a very good nanotech program, probably the best in the country (maybe even the world) in topics involving carbon nanotubes. If you are in the midwest and are looking for a college that isn't way out on the coast it is your best choice by far. They also let undergraduates help out with research, although you probably won't be doing much on your own (maybe as an upperclassmen....maybe). Also, check out this program, which I did this summer and you can do in 2 summers. You get to go to Japan for 3 months and research nanotechnology in a Japanese laboratory. I research semiconductor fabrication and learned a TON!
www.nanojapan.rice.edu Top notch program!
Anyway, nanotech is a HUGE field (ironic, huh?), so there's a lot of different applications. Nanomaterials seem to be the most promising field and are making the largest progress, in my opinion.