I think getting an engineering degree is an excellent idea if you want to pursue professional aviation. I graduated with a degree in mechanical engineering, and was able to get a decent paying job pretty quickly. While working full time, I flew on the side and paid cash for all of my ratings. I also paid off all of my credit cards, my car, and non-subsidized students loans. I also created a savings account cushion before jumping into professional aviation as a CFI. This really took a lot of stress off me financially, and it allowed me to enjoy a pretty good quality of life when I was still really low on the aviation career ladder.
It does seem somewhat strange to me that so many people on here are quick to dismiss the benefits of having an engineering degree when applied to aviation... Weather, systems (hydraulic, electrical, fuel, turbine engine operation, etc.), technical rules, aerodynamics, ability to stay focused and organized, etc. These are just a few areas in which my engineering degree has benefited me with aviation. Is an engineering degree REQUIRED to understand these subjects? Of course not... Does it help? Absolutely.
As far as a backup career, "ILSstud" has a point about facing difficulties getting back into aviation if you've been flying for 10 years. But you can always go to grad school for two years and become very employable in a relatively short amount of time. Your time spent flying could also be looked at very favorably in some segments of aerospace engineering (field/service engineer, avionics, test engineering, etc.). It would also be wise to maintain your professional contacts over the years, and you could even look into doing some part-time engineering work on the side to stay current. Either way, it's going to be MUCH easier to land a job with an engineering degree than some generic major like communications or something.
I worked as an engineer for about five years, and am now closing in on my third year of professional aviation. While I do feel frustrated sometimes with the aviation industry, so far it has treated me pretty well and I am MUCH, MUCH happier going to my flying job than I EVER was my engineering job. Still, I wouldn't have changed how I did it at all. Good luck, and feel free to PM me with any questions!