There are, roughly, two types of programmers. One type was in the computer club at high school and got a computer science degree (or two or three). The other type, well, didn't--they were English majors, college dropouts, busboys, artists, odd-job-doers. (Cue Captain Renault: "That makes Rick a citizen of the world.")
My advice to young people is to get a computer science degree, if for no other reason than you can avoid those odd jobs and get right to the programming. And it also gives you an early chance to find out if you were, in fact, born a programmer.
In my experience, in general, I prefer working with individual programmers who didn't get a CS degrees. That's not universally true: there are some CS-degree holders I love to work with. And it doesn't imply a particular causal relationship: it could be that people I enjoy working with are simply those who are less likely to get a CS degree, rather than my enjoyment stemming from the fact that they didn't.