Once an applicant has some experience under his belt, it doesn't really matter much about formal education. If you've worked in a respectable development environment for a few years, then great - come to an interview. I may ask about your background in your interview, but mostly to see how you handle discussing your background.

But if you're at the beginning of your career, and have little-to-no experience, then you'd definitely struggle to even get considered. Think of it this way. All applicants will have an interest in and a knowledge of programming (while this is not necessarily true, it serves for the purpose of the analogy). Of those, almost all will have secondary school level qualifications (A Levels here in the UK, High School in the US). Of those, some will have a CS Degree, and of those who don't, some will have experience. Those are the ones I'd consider first.

As someone with no experience and no qualifications, there'd be nothing on your CV to make you stand out as someone worth hiring for the job. From a recruiter's point of view, programming is an academic discipline, so school-level qualifications are vital in order to show that you have the discipline and ability to learn; even if your educational background is not in CS.

But on the other hand, the company I work for (which I won't name, obviously) is an IT Consultancy firm who specialise in recruiting people (often graduates, but not necessarily - each applicant is assessed on an individual basis), providing ~3 months of free but unpaid training, then hiring people out to blue-chip companies for the next two years. Companies like this are becoming more popular around the world nowadays (this one is based in the UK, but has offices in the US, Germany and Hong Kong); so while you may get laughed out of the room when applying directly to big companies, there are alternatives to help kickstart a career in programming.
The philosophy behind the company I work for is that for fresh graduates, it's near impossible to get a job in IT, since even the most junior positions require 2 years experience normally. So companies like this benefit young aspiring IT professionals, by getting them 2 years good work experience, and relatively up to date training; and also the companies they hire out to, by providing consultants of a known standard of quality, reliably, and without all the HR hassle of directly hiring people.