Ask HN: Would you hire a dropout?
Assume that they
1) Are fully qualified for the position, and
2) Dropped out to purse self-employment/self-education/work, not because they couldn't handle school
Then again, I'm biased.
A proven track record of being self motivated and being persistant with their goals are far more valuable traits in an individual than a piece of paper saying they went to some college or university for several years.
I try to shun away from dropouts because school signals, more than anything else, an ability to slog through tedious tasks. And unfortunately, not everything you will do is glamorous.
The only reason I accept for dropping out of school is money problems, but even then I trust those people more who will work on the side of their studies.
Remember anyone can program, not everyone can find a solution.
Skills and an apprenticeship under the right mentor trump the piece of paper in terms of real world results. It's really tough for more conservative types to realize this until the researcher in question is so famous that they no longer have a chance of hiring them, though.
Any difficulty distinguishing people with and without 1 is more important, but is present regardless.
The problem for most jobs that "require" a degree is that a degree signifies a minimum knowledge base and experience with the subject matter (if not practical experience) of the position. The point at which work experience becomes more important than having a degree depends heavily on the position. Thus, for example, work experience will probably always be more important than a degree for something like design, but a degree may be more important for starting out in development (assuming that you do not already have work experience in the relevant areas).
Further: people in my industry tend to pursue a formal education, work, and/or self-education simultaneously (or at least two of these options). Any candidate who couldn't handle work and education simultaneously would simply not cut it, unless they opted for work because they could not afford to work and pursue an education at the same time.
Unless the candidate was too poor to afford the school, or born in the 3rd world, or something like that, there's not much excuse for not having the piece of paper.
If you decide to hire the dropout, you are gambling on "this guy dropped out because he's the next John Carmack, not a loser". The odds are poor.
ADDENDUM: The degree acts as an arbitrary filter because you simply do not have the resources to exhaustively examine every candidate. you only take a closer look at the candidates that make it through the filter.