A degree helps, although it isn't required. I look to see if someone does have a CS degree whether its a bachelors, a masters, or a PhD but in the end, just because they have one, doesn't mean I'll hire them. It does depend on more than that and if I find a talented programmer I believe in, I could care less about the degree. As a few people already mentioned above, the key when applying for a job is extensively listing your skill set and programming languages you have. BUT, to take it a step further, you should always include a cover letter mentioning things you've done that may not be job related, things like pet projects, stuff you've coded for fun, or complex things you've built to demonstrate your capacity for coding. A resume will never reflect those things. And of course a portfolio is vitally important, something an employer can see and feel for a sample of your work.
Having said the above, a few other things to note. A skillful programmer who is absolutely passionate about programming, and all they do is talk shop and dream of programming all day and night shows. A lot of people like programming, but they don't love it. They do it as a means to a job and not as a hobby outside of work. The programmers I've worked with live and breathe code at work or at home. These people are the people who solve great problems on the job. Ideally what I want is someone who can learn and adapt fast. Pick up new languages if they must, program apps if they have to, etc.. These are qualities people want rather than someone who is a great master of any given language. I also care greatly about how well a person can document code and how secure they program. How fast they can scan code if needed and see problems within the code. A typical resume won't detail this stuff.
Lastly, of course, what languages they know and how well of a fit the criteria I'm looking for. A normal resume may lack this and I won't really know if someone can pick up the past when challenged and hence why the other stuff is important. Unlike another person who mentioned certification, no one I know really cares about those things. They are easy enough to get and at the end of the day don't mean much. The quality is in the programmer themselves. I can tell you I've scan through hundreds of resumes and it is extremely difficult to find even one person who becomes a good fit. I'd honestly kill to find the right programmer. Still do. To date, I've only found about 3 people among countless resumes that come through. And believe me, these programmers are definitely elite in their own right and it shows through work they've done or work they're able to produce.
I should also mention I'm big on hiring full time employees and they must be local. I don't do telecommute or contract base positions and I'm sure a lot of companies are the same way if they had to choose.
This post has been edited by nooblet: 16 May 2010 - 07:18 PM