It's hard to think of many things less resonant with the HN crowd than Jung. But this is a good article about a pivotal event for anyone who is interested in him.
Jung provided the underpinnings of Joseph Campbell's works on story and story structure. He essentially reverse-engineered story and laid out design patterns that nearly every story follows. I've found that the study of this concept is a very rewarding one in terms of appreciating and understanding movies, video games and any other media that represents a story.
Jung was a mystic whose work is largely an articulation of traditional religious and symbolic thought in modern terms. Although he always called himself a scientist, most people nowadays would consider that a silly claim. (He did some experimental work in his early years, but nothing related to Jung qua Jung.) Rather, he was as close as you'd get to a shaman in a respectable early 20th century Swiss doctor. If you like the idea of a magical dream-world with completely different laws than those of the physical universe, Jung's your man.
Accordingly, Jung is incongruous with the technical/scientific bias of the HN crowd. I'm sure there are a few people who are or would be interested in him, but if posts about the likes of C.G. Jung ever became prominent here (which they won't), they'd get ripped to shreds. If you doubt that, go read his foreword to the I Ching.
Personally, I think Jung is fascinating and his ideas in some ways are attractive, though I could never figure out how to actually make use of his writings.
Jung's writings do often give the impression of importing mysticism into science or of mysticism for its own sake, an impression sustained by some of his critics, supporters, and this (fairly good) article.
However, after reading most of his collected works, the overall thrust of his work seems the opposite -- to grapple deeply with the mystical and have it yield to the conscious, probing tools of analysis (if not quite science).
In the Jungian view, myth, folklore, archetypes, scripture, and dreams are common artifacts along the path towards understanding unknown, threatening things. Rigorous analysis (the article overstates this when comparing this to solving quadratic equations) can yield insights into what unknowns an individual, culture, or organization is grappling with and the progress that has been made.
Hacking and startups repeatedly put people on the edge of what is known; a hacker's daily trade is in conjecture and hypothesis. When things work well, conjectures can be tested definitively, safely, and in small pieces; therefore the unknown can be conquered routinely. When that is not possible, hypotheses solidify into myth and legend, and progress can still be made. But a startup has to be able to break down and understand those myths over the long run, salvage what is useful, and discard what is not.
That's a valiant attempt to connect the dots from Jung to startups, but if you're willing to be that arbitrary you can connect anything to anything.
the conscious, probing tools of analysis (if not quite science)
There's no "quite" about it. There is an enormous intrinsic gap between analysis as practiced by Jung and science in the modern Western sense. That's not a criticism; I am no idolator of Western science (and have been a fan of Jung for years, though not of Jungians). But let's not pretend that Jung's writings would find any place in a peer-reviewed experimental journal.