Not important in the slightest when it comes down to it, really.
Heck, lots of the best software engineers I've worked with or hired either never finished college or had never taken a computer science class in their life (the physics programs at some universities have tended to produce exceedingly good software engineers in my experience).
Now, I'm a little biased since I'm one of those people that never really took a computer science class, and never finished college... and while I was there, I was a business major.
Now, that being said, some people really do benefit from some computer science programs, and they can be valuable, just as soon as those who have gone through them realize one or both of the following:
- They still have a LOT to learn, and knowing how to "program" is a long way off from being a competent software engineer
- They're going to need to forget lots of what they just learned
With real entry level people that would be coming to work for you straight from college, it can be pretty tough to weight their resumes since the "education" section will be so prominent compared to the "experience" section, although if you're getting good submissions along with some sort of cover letter or note, or, better yet, answers to some sort of little test or other question(s) instead of JUST their resume, this is made far easier. That should be enough to at least decide which ones to interview, which is where the real decision is made anyway.
To sum up, no, having a degree is really in no way any kind of accurate measure of how "good" somebody will be, skill-wise, and I can guarantee you that if you throw out any resumes that don't have a degree listed, you're going to pass up some real gems.