ANGC 13: because it requires a great drive to set up a good chance to go for the green in 2, even with a great drive it makes you decide on going for it or laying up, because even a layup has to be well placed to give you a good chance to hit close to the pin and because the green is a lot of fun to put in. It also changes quite a lot depending on pin position. The hole plays as good for amateurs as for pros.
This....
I've never played it, but don't care if that downgrades my opinion. While there are many great par 3s, they tend to be limited in how they play, with perhaps an exception or two (Cypress Point, which is a contender here). There's many great par 4s, some mentioned already. But the first hole I thought of was this one.
Why AGNC's 13th?
-- It has always struck me as one of the great option-filled, risk-reward holes ever built.
-- It's natural in appearance and -- save for the green contours -- in fact (as opposed to natural looking that's been concocted). It follows the flow of the creek, takes into account the terrain of the course, and has one of best-placed greens I've seen.
-- The green is all-world, certainly a must for any hole that's in the running for best hole.
-- As noted above, it's a hole that delivers a test for all audiences intended (the best tournament in golf, and regular member play).
-- It can be both severely penal and hugely rewarding, and unlike nearly all par 5s, has a thoughtful and even fear-enducing 2nd shot, with recriminations all around for how that 2nd shot is played.
-- It has options off the tee, options for the 2nd shot, and all manner of decisions for the golfer to make depending on the outcome of those first two shots.
Given one hole to play, anywhere anytime, I'd take the 13th at ANGC in the spring.