I once "taught" a previous boss how to do them, learning some basic crossword type things ("perhaps" will often indicate an anagram etc) and then looking at the answers the next day to try to find the link between clue and answer.
Some are very perverse, but can lead to extending the mind, for example I now know that Veronica is not only a womans name, and the name of a plant, but also a move in bull fighting!
And before anyone posts, yes, I do know that that bit of info is hardly likely to enrich my life or be much use in day to day events, but so what?!