If you have no experience, then a degree might help get you in as a junior developer somewhere. With even 1 year or more of experience (real world, not just lab assistant type) the degree isnt important at all (at my company). It doesnt look bad, but its much better to see 1 or 2 years of VB.NET, C#, Database, or something else "useful".
There are SO many factors into hiring someone though, its hard to pin one area down as more important than another. Personality is a key (must get along with others) for instance, though many companies wont mention it because its too taboo (it could potentially be used to weed people out by race, sex, or whatever else people might not want). But if youre expected to work as a team, you must get along well with everyone in it.
-Ner