Ok - I'll bite. The answer to
|What is the most important shot in golf"
is "It depends." I'll raise Mike's two thoughts and go for three.
My first thought is "the last shot" because that shot is what determines the score on a hole.
My second thought is that it depends on situation. Stroke play is a different game than match play. The last shot does not make a difference in match play if your opponent is already in with a lower score. But what is the benefit of designating levels of importance to shots? Each shot played counts the same towards the score. But some shots can "cause" other shots to be forced onto the score either through the result of the ending location or through penalties. Other shots can cause a reduction of planned shots (e.g. a long drive on a par 5 can enable reaching the green in two or a close approach shot can enable a one putt). Can you rank the importance of a shot by the probability of the addition of extra unplanned strokes or subtraction of planned strokes as a result of it?
My third thought is that it depends on the psychology of the player and the situation. One benefit of assigning importance to a shot is to positively effect future performance. The thinking here is that one will put more effort into a shot that is more important. But some people perform worse under pressure. Telling them a shot is not important may get better results. Other folks, no names mentioned Tiger, perform their best on the most important shots. How many of us have played better after starting a round poorly because we no longer cared about the results because the remaining shots were no longer important?
While achieving the lowest score possible is desirable, many of us derive pleasure from the game from other factors. Whether it's winning bets, making long drives, being closest to the pin, making difficult shots or fixing problems, there are many different possible "most important shots" that have little to do with the strategy required for the lowest overall score for a round. For example, because I've been dealing with a shoulder problem, my most important shots right now are deep rough and bunker shots. If I don't execute those shots correctly I get significant negative feedback.
Further "most important shots" can vary depending on whether one's goal is to go low for one round, multiple rounds, or achieve the lowest possible handicap. Course management involves making risk reward tradeoffs. One may get the lowest possible score on a hole for a single round by aiming straight at the pin, but get a lower aggregate score on that hole over multiple rounds by playing more conservative approach shots (e.g. aiming for the center of the green instead). With the riskier strategy, the approach shot is more important. With the conservative strategy, the first putt is more important than the approach.
I love these kinds of questions. We get them a lot in ski instructor clinics. It's easy to misinterpret these discussions as a quest for the "right answer" (even when the asker is looking for a "right answer"). For these kinds of questions, the right answer is never more important than the discussion. It's the discussion that increases one's understanding of the sport regardless of the answers.