This is a fun question, and I finally found a clear-cut winner last year, only to be rivaled by one that occurred this past Monday. I've had about 20-25 eagles in the past 6-7 years, including one from 185, but I feel like alot of these are a solid shots combined with dumb luck. I think the best shots are the wild shots you envision in your mind's eye previously, so here goes:
Hole 15, Old North State Club in NC, par four. My tee shot trickles into the right fairway bunker, about 140-150 yards from the green. As I get to my ball, I see that it has come to rest about 18 inches from the left edge of the bunker, the sand surface being about 2 feet below the level of the surrounding rough. This lip continues around the left and front of the bunker on the line to the green, which sits on a small rise, bunker short left below the green, fairway leading to the surface at the front right. While seeing if I can even hit this ball, the only way i can stand is with one foot in the bunker a few feet behind the ball, and the other 2+ feet above in the rough. To make matters worse, I cannot seem to stand without my body wanting to fall over. I finally get settled, my body tilted away from the ball at something like a 45 degree angle. I have chosen a 4-iron for the shot, the only club with which I can reach my ball, due to my ridiculous stance. Maybe the ball will somehow have a chance of running up near the green if the lip is cleared, but not a very realistic goal.
So i swing back and through, barely skulling the ball with the open-faced club, the clubhead slams into the bunker lip and i go backpedaling into the bunker. The ball shoots out like a rocket, and slams into the rolled bunker lip directly above it. However, the blow is glancing enough to change the spin of the ball from dead-pull to left-to-right, the ball slices about 40 yards as it flies, lands just above the greenside bunker, and rolls onto the green, about 15 feet from the hole. I would have been happy to just get it away from the lip for the next shot from the bunker. Probably my best shot ever.
My competitor happened just this past Monday at Jeffersonvilee in Philly. Two or three times a year I pull the wrong club from my bag by mistake, when I'm not paying attention or I'm distracted. This is what happened on #4, the 140-yd par three. The pin was in front, and I wanted to hit an easy 9-iron. After hitting my well-struck tee shot into the grassy depression short of the green i noticed I had mistakenly pulled my wedge. So, just for kicks, I teed up a second ball with the 9-iron I really meant to hit. I'm sure you can imagine what happened. Landed 4 inches too far, but spun back. Jar. Saddest "par" ever.