In my experience just about everybody fancies themselves a great programmer and considers anybody who doesn't know (insert semi-random list of skills) to be a shitty programmer.
I kinda think it's like the Roth test for obscenity. I can't really explain what makes a shitty programmer, but "I know it when I see it."
Most people I've worked with over the years have understood their limitations and would never consider themselves great, with the possible exception of half a dozen or so folks, who truly are great.
My opinion is probably tainted by my own working experiences. I've run into various mediocre IT pros who have been at it for a while and possibly are trying to appear smart for purposes of job security.
I've only had the pleasure of working with a handful of what I considered truly great programmers. I don't think a single one of them considered themselves to be "great" even though I thought they were.
I kinda think it's like the Roth test for obscenity. I can't really explain what makes a shitty programmer, but "I know it when I see it."