It depends on your school. People generally do double majors or minors for these reasons:
It's free or easy to pick up - many engineering majors will grab a minor (or even a major) in math, physics or chemistry. Check to see which of these you can get with no additional classes, or very few.
It compliments what you want to do with what degree you want - Chemical Engineering and Biology for med school, management and engineering, etc.
A job requires a degree in field x, but you really want to do y. Do both.
In many schools, you may find that CS or SE are the same, or there's only one. Looking at recent job descriptions, CS and SE are the same.
I'd suggest that get a major or minor in whatever you can get for free or little effort. The CE is the top degree, the others are 2nd.
Consider a major in something else like math or physics to compliment - do you want to work for the NSA? Then CE and Math would get you in fairly well. Do you want to work on the Large Hadron Collider or Tokamak? Then physics would probably help.