Allow me to warn you. This is one of my sole bigotous traits. I am a bigot when you talk engineer vs coder.
My answer? Depends on the degree. I'm a programmer (actually, I prefer the term 'developer'), and I have a degree in computer engineering. I am an engineer. I have co-workers that have degrees in EE. They are engineers. I have co-workers that have degrees in CompSci and Math. They are not engineers.
Do not get me wrong. Some compsci/math majors are better programmers than some engineers. But they don't have the background in engineering. Engineering is a type of thinking, and a type of problem solving. These techniques are pounded into our heads with every engineering class we take. It isn't easy. I've seen over half (almost 3/4s) of my class drop out. I didn't. I pride myself on that piece of paper that states I'm an engineer. I hate the fact that other people can put it in their title (a la "Software Engineer") and dropped out of engineering for a different degree in college.
Some states require you have an engineering degree before you can have a business title with the term 'engineer' in it. Some states require you have a PE[1*] before you can have the term 'engineer' in your title. I support the first one (the second one is a bit outdated IMO).
So there you go. FK can be a bigot/zealotous himself. Feel free to flame or argue with me, but you'll find I'm pretty stern in my stance.
[1*] a PE is a 'professional engineer'. You have to take a test when you graduate (which is extremely difficult), then take a second part of the test after you have been on a job for over 5 years. If you pass both, you are given the title 'Professional Engineer'. The biggest reason for a PE was for the courts. A 'PE' could be called as an expert on a particular engineering field. There were other reasons (like extra resposibilities and liabilities when you have it), but that was the biggest. Now-a-days, you get a PhD to be an expert and 'PE's are rarely seen (I didn't bother taking the first test), and are a thing of the past that will die away soon.