I am graduating with a BS in Computer Engineering this spring. I'll be doing software development as my first job. My other offer was a little different, but still doing software.
Agree with the above: You can take at least a years worth of general engineering courses without getting specifically into Electrical, Computer, etc and not fall behind.
Actually I read the rest of the thread, and I agree with pretty much everything else said. You aren't required to have basic programming skills upon entrance to a CpE or CS program, but it will help you. Here you can take an accelerated Intro to CS class that replaces two separate semester classes. It doesn't matter what language, just knowing some basics will get you a better grade and allow you to be pounding beers on nights when the rest of the freshman CS kids are in the labs.
Places like AMD or Intel hire Computer Engineers, but I bet it is very tough to get hired there. See this thread:
How hard is it to land a job at such places like Intel/AMD/ATI/NVIDIA ?
I don't have the experience or knowledge so I didn't bother applying at any such places. To do any design, you'll need a more advanced degree probably. I'd also think they hire mainly from a few select schools. So it certainly is possible, but I bet it is very difficult. You might be better off as a EE with either (a) a digital design concentration or (b) as a physics/semiconductor concentration. EE semiconductor physics is something I don't hear many people going into but definitely a good choice if you like physics and such more.
A friend of mine graduated last semester as an EE with a Materials Science minor. Either he had classes or he knew about mining and materials and such. He had no relevant experience and like a 3.0 GPA, and he had a bunch of offers, one he took for almost $70k. So the material engineering is definitely sought after and lucrative. I don't think many new grads join mining and related companies, sort of like the railroad companies, so you can actually make awesome money and have a job for sure with things like that.
So I guess in conclusion, there are lots of good engineering degrees to major in, some relating to computers a lot, some just a little. You can always play with computers or write some software on the side, even if you do something not at all related to them.