Which hardware do you want to design? If you want to design CPUs I would recommend a degree in straight up computer engineering. I'm sure electrical engineering or a physics degree would do it as well. Computer engineering involves software/firmware design and hardware/software integration as well so it's probably the best. However I do know intel/AMD employ a ton of physicists for R&D. I do know AMD does internships, and that would be the best way to get your foot in the door!
The thing I would be concerned about with any other engineering degrees is there is the possibility you'd end up just doing fabrication instead of design. Which is really boring.
Hey BrittBrannan, I was just checking out your hub, and I just want to let you know that I find it very interesting. I have always really liked writing and computers, and hope to learn more about programming someday soon. I sure wish I knew more about comp. repair myself, so I wouldn't ever have to worry about my comp. breaking down. If you ever happen to have any more interesting data to share my user name is EricBr