Considering all the excellent counsel Doug gives, I feel ashamed for telling you this ... I don't have a degree. I have lots of college credits, but never finished the degree program.
Since this website's primary purpose is to educate and encourage aspiring pilots I must strongly agree that the degree is of utmost importance. Can a pilot make it without one ... maybe, heck I have, but the reality of the degree will open doors and get you in doors I will never go through. I have been extremely fortunate and some may say lucky, but if I had to do it all over again I would have finished college first. I came from a different background where education wasn't valued and the encouragement I received was to learn a trade. I worked, and I mean worked, in the plumbing and heating trade for 10yrs before breaking into aviaition full time.
Without hesitation I would recommend a degree over taking chances of being the exception to the rule.