Suppose a position along these lines, where W does not answer the marked play, perhaps taking a huge ko instead. How should B continue?
I (8?k) would extend 4 to a which I think is entirely safe and a nice extension. When I recently did this in a game, it worked fine but the opponent was about my level so I am not certain this is the best move.
I have seen people, including players stronger than me, extend only 3 to b and I recently saw a pro game with a 6-point jump to c. What is the right extension, or if "it depends", then what does it depend on?
As the previous reply shows, the two space extension (to a) is not safe from being cut off. The one space jump to b would not be cut off this way. Unfortunately there is no simple description of when an extension is safe from being cut off, it is highly dependent on the arrangement of the opponent's stones. There is a lot of relevant information on the page monkey jump and on the pages linked there. More detailed information is in the book Monkey Jump Workshop by Richard Hunter.