Certainly, being a self-taught programmer and self-teaching your way through a CS degree are different things. Likewise, Computer Science as an academic field and Programming as a career are different. Other responses have mixed this up... expecting someone trained as Computer Scientist and to be good at programming jobs is, I think, silly.
The CS department at my Ivy league school did not teach very much that would qualify the students (my peers) for work. In light of that, I consider myself a self-taught programmer, even though I have a diploma with a CS degree from my school.
So, I don't think that it's about having a degree or about (claiming) to be self taught. If you are applying for a programming job, it's about your programming portfolio, wherever and however it exists.
I find that most programmers who are only self taught are missing breadth. They're great with what they encountered and had to try, but usually suck at even knowing of the existence of what lies just beyond the edge.
Or at least the ones I've had the pleasure of talking to :)
That is one area where the internet could use improvement.
Google can teach you anything... if you know what you're looking for; but there doesn't seem to be a good system for exploration beyond that. If you follow the right discussion/link services and keep a general watchful eye out, the stuff out beyond the edge will eventually flow to you, but there is certainly room for improvement.
I believe it is a solvable problem and the company that gets it right will have amazing growth potential.
http://en.wikipedia.org/wiki/List_of_algorithms
You can also look up what textbooks are used at major universities, then look up their tables of contents on Amazon or Google Books.
In general, one nice thing about hiring CS students as opposed to purely self-taught programmers is that, in my experience, they're more likely to have a good understanding algorithms and data structures. Self-taught coders often only learn as much as they think they need to know about the topic to complete the task in front of them. (Obviously, for those interested, it's as straightforward to teach yourself analysis of algorithms as any other topic.) For some types of programming positions, having a rigorous background in this area is crucial, though in others not so much.
[1]: For what it's worth, I was a junior when I dropped out of my bachelor's degree in CS program, but over the years I've accumulated 3 associate degrees: General Education, Computer Programming, and High Performance Computing, and have studied all sorts of stuff on my own time... just because it's what I found interesting. And I still work on learning new stuff each and every day. <shrug />