One reason is what you might call signal-to-noise ratio. Sure, there are talented techies out there who don't have degrees. But put yourself in the shoes of a hiring manager for a minute. You post a job that says "BSCS required" and get, say, 250 resumes. Maybe 25 of those people will actually have the combination of skills, experience, intelligence, motiviation, teamwork, and so on that would make them a successful hire onto your project. (Obviously I'm just making up these numbers for the sake of illustration, but bear with me.) Your job is to figure out which person or people should get offers.

Now you post a job opening that says "no experience or degree required". You get 5,000 resumes. Undoubtedly some of those folks that don't have the degree or the experience would make great additions to your team. But it's going to take a lot more work to find them.

Also remember that many companies use HR departments to do initial screening. There are HR people who have enough technical knowledge to understand specific technical requirements you might have for your hires, but that probably isn't the norm in most environments.

So the degree requirement basically sets a filter that presumably improves the proportion of applicants that are potential hires. It doesn't mean that any particular individual with a degree is a better candidate than any particular individual without one, but it probably means the overall quality of the applicant pool will be higher and you'll spend less time and money on your search.

Another thing that requiring a degree -- any degree, CS or otherwise, from a reputable institution -- does is to ensure that applicants have a certain baseline skill set. That includes things like reasonable writing and communication skills, which can be nearly as important in some environments as actual technology acumen. The degree presumably also indicates an applicant possesses a certain amount of motivation and endurance. Again, that's not to say any of these qualities are absent in someone who doesn't have a degree.

Anyway, this isn't meant to be discouraging -- as other posters have pointed out, the absence of those two letters on your resume needn't be a career death sentence. I just wanted to see if I could provide some perspective into what probably seems like an arbitrary and frustrating hiring criterion.

By the way, if you do good work then I'd suggest using networking (i.e., personal contacts) as much as possible to get in touch with people who might be hiring. As a hiring manager, a recommendation by someone you know and trust who can vouch for the quality of a candidate's work will be worth a lot more than almost anything that could appear on a resume.