I'm changing my answer - worst is a great shot, you see it fly, you see it land, and when you get there, it's nowhere to be found.
For me, sitting pretty in the fairway with the green right in front of you, ready to be attacked and then proceeding to hitting the ball PURE but pulling it dead left and long. The boils my blood more than ANYTHING.
A couple of other things that come close. Stupidly blowing a 10-15 foot putt past the hole, and missing the putt coming back - STUPID! Another, hitting your second shot greenside on a par 5 and then duffing your chip onto the green. You feel great that your second shot was hit well and is off the green in a reasonable place and then duffing the chip completely ruins it all. You were excited to chip and have a putt for birdie, now the second chip is under pressure because you don't want to make a bogey.
The dreaded missed short putt, just ask....
Scott Hoch: It's every golfer's dream: You have a tap-in putt to win the Masters, earn a green jacket and forever be a part of golf history. In 1989 that scenario became a nightmare for Scott Hoch—he missed a two-footer that would've won the tournament. Nick Faldo shot 65 to tie Hoch and won the green jacket with a birdie on the second sudden-death playoff hole.
Doug Sanders: Winning a major is a life-changing event for any golfer. Doug Sanders missed a short putt on the final hole of the 1970 British Open, ending up in a tie with Jack Nicklaus. Nicklaus defeated Sanders in an 18-hole playoff the next day.
Ben Hogan: At the Masters in 1946, Ben Hogan needed a par on the final hole to get into a playoff with Herman Keiser. After a missed birdie attempt, Hogan lined up a two-footer to tie—and completely missed the hole. (Keiser retired in the 1950s, having won five tournaments during his PGA career. His only top ten in a major was his victory at Augusta.)
Sam Snead: Snead holed a heroic birdie on the last hole of the U.S. Open to force a playoff with Lew Worsham. After 17 holes of the playoff, Snead and Worsham were tied. On the 18th Snead's approach shot stopped pin-high and 15 feet left of the hole. Worsham was long and lay 40 feet feet past the cup on the apron of the green. His chip rolled into and bounced out of the cup, ending up 29 inches from the hole, which left Snead his birdie putt for the win. He left the putt well short. Just as Snead attempted his par putt, Worsham asked for a ruling to see if Snead truly was away. He was, and when Snead finally hit the putt, he missed. Worsham didn't.