What types of higher than undergarduate degrees look exceptionally good relative to other equal level degrees?
Those stories exist, but not all of them are true. Be careful and look at the source of the story: Does it come from the institution itself (who is trying to "sell" its program), or from someone who is trying to make her or himself look important by telling about the wonderful job offer(s) they received? Also consider if this is it a selection of success stories or if this somewhat representative of the experience of all the students who finished that course.

Moreover, even if a field of study is now lucrative, that does not mean that it will still be lucrative when new students finish their education. Pork cycles are a big problem for many fields of study.