Looking on youtube, I see a number of videos of jump/dives from a height of 100 feet. One is also tittled “38 m (125 feet) high dive goes wrong” (however, despite clearly fumbling, the guy isn’t even seriously wounded).
I couldn’t find a world record or such a thing.
What if you had a large rock about a metre in diameter, and you followed that down a couple of seconds behind? The rock would hit the water, punch a hole in the surface, and decelerate. Behind it would be a temporary area of mixed air and water, and you could land in that. 
Actually you land on the rock, since it’s suddenly slowed down and you haven’t - yet.
The best you could do was spread yourself out as much as possible during the fall to lower your terminal velocity. Also, hitting the water flat spreads the force impact over the largest area of your body possible, ensuring everything gets injured somewhat rather than whatever hits first being utterly pulped.
What if the object were dense and pointy and could penetrate the water? Say, you were about to bail out of your plane at 20,000 feet, and though you didn’t have a parachute handy you had a large depleted uranium artillery shell.* Grab the end, jump out of the plane and point the shell (and your head) straight down. Those suckers are designed to penetrate concrete bunker walls – would water be denser than that? If you’re worried about it, though, perhaps try letting go of the shell and putting yourself feet first again right before impact.
*for some reason
In auto accidents they talk about first, second and third impact. First is the car hitting another car or object. Second is you hitting the inside of the car. The third is various critical organs in your body hitting the side of your body. Injuries like your heart tearing loose from its main blood vessels, brain hitting the inside of your skull, and so on. It isn’t the external blunt trauma that kills. It is the deceleration, and trauma on the inside. Thus the earlier advice, spear into the water feet first. The water drag on your body will decelerate you fast enough that you still may not survive, but broken feet are a heck of a lot better than spending the last few seconds of your life with your heart trying to dig a hole in the side of your chest.
Yes, anyone who has been canyoning or coasteering (which involve jumping into water from heights up to about 50-60ft) will know that you are told to enter the water pencil straight, with feet crossed over each other and arms crossed over the chest. The smaller the surface area you can present to the water, the less the drag will be and the slower you will decelerate. Slower deceleration means less chance of injury.
Not that entering the water like that would do you much good if you had jumped from 20,000ft though. Presumably to maximise your chances of survival it might help (a little) if you spreadeagled yourself to increase drag and reduce your terminal velocity while in the air, then adopted the “pencil” position just before hitting the water. Good luck trying to time it right though…
Any flat surface pointed straight toward the water will experience maximum impact pressure. This is why things like airplanes are pointy and gradually taper to their full diameter: there is reduced ram air pressure on the tapered region, far below what it would be if the plane had a flat nose, resulting in minimal drag.
The ram pressure experienced by a flat surface impacting the water is calculable: at 120 MPH falling into fresh water, it’s 208 psi. Your face is, what, 5x6 inches = 30 square inches? So that’s 6000 pounds of force, just on your face. Your sinuses will implode, your lower jaw will probably break, and I imagine even your front teeth will be shattered out of their sockets. Imagine similarly horrible things for the rest of your body.
Just like that tapered airplane fuselage, it’s far better to fall feet first, and point your toes downward. Ideally, that highest pressure would only be experienced on the tips of your toes, with lower pressures along the rest of your legs and body. The reality is that it will probably be difficult to keep your legs and feet pointed down once you enter the water, and that’s when injuries are likely, at least to your lower body. Expect broken legs, feet, and/or toes, hyperextended/dislocated hip joints, and possibly spinal injuries. In spite of that, this still gives better odds than landing in a flat, face-down orientation. Your internal organs and brain will be decelerated far more gently.
My first thought was, “Use a parachute. Duh.”
Yeah, I’m packin’ a chute in my carryon from now on.
But thanks, all, I’m ready to fall over an ocean. Only one ?: Do I tuck my chin down, too?
Though it has already been mentioned in previous linked threads on the subject, Guinness does list Harry Froboess as surviving an intentional leap of 110 m into Lake Constance, Switzerland. I had a difficult time finding any documentary evidence of this high dive, and I have my doubts that it happened as described. Froboess was a renowned movie stuntman, FWIW.
He wrote two books, per wiki, which are unavailable on Google Books. Nor have ever seen them anywhere. Perhaps more information on his leap is available in one of those books.
The links, physics, and forces calculation discussions, from you all have been very interesting, thank you.
Terminal velocity depends on a number of things including body position but for your generic belly to earth arch (the classic skydiving freefall posture) wearing clothing that is neither tight nor loose and baggy it’s reckoned at about 120mph and takes about 10 seconds and 1000 feet to reach that speed.
As a ute, I grew up in Evansville, IN.
My sisters are 7 & 10 years older than I am, and under orders not to leave me home alone. Thus, at 10-12 years old, I found myself accompanying my sisters and their boyfriends (17-22 years old) to the local abandoned pit mines that are common in Indiana.
These holes in the ground in the middle of nowhere were huge. Hundreds of feet across, and who knows how deep. Fed by rainwater only, they were clear, warm, and still.
The older boys would climb as high as they dared, and jump in. Naturally, I did what they did, and it was awesome! You kept your shoes on, and jumped feet first, doing a pencil dive. Once under, you spread your legs and arms to slow your descent, then struggled to the surface. There’s a thermocline at 15 or 20 feet, and you shoot right through it, feeling the cold water rip up your body. I estimate we would sink 30 feet or more before beginning the swim up.
I went back to Evansville years later, and actually found one of the quarries.
I stood and looked at where we jumped and almost fainted. I remember quite clearly the ledges we would pick, and I stood and measured (guess-timated across the way) that we jumped from 30 to 80 feet high.
None of us ever felt any ill effects, but man, kids are dumb.
My experience of doing roll exits from speeding boats while fully dressed is that it feels like hitting concrete with your back.
Obviously it isn’t, but its not an incredibly pleasant experience.
I’ve always wondered what would happen if you were already in the water - say, you had breathing gear and were inside a very large container of water, and the container fell to the ground, would already being immersed in the water cushion your deacceleration?
Assuming you were overall neutrally buoyant - that is, your overall density was the same as the water around you - you would expect to move exactly as the water moves. That is, you would not move toward the top or bottom of the tank. With hydrostatic support from the water, you shouldn’t feel injuriously concentrated loads on any one part of your body.
Things get more interesting when you take into account the fact that gas pockets in or on your body would compress because of the increased water pressure during the deceleration event. As the body of water decelerates, the hydrostatic pressure on your body would increase accordingly. When the tank is still, you experience a certain pressure proportional to your depth below the surface. If the tank decelerates at 1 g, the pressure you feel during that deceleration event would be double what you felt if the tank was falling at a steady speed. This means:
-your buoyancy compensator (a vest you wear with pockets that can be inflated or deflated to adjust your buoyancy) would decrease in volume, reducing your buoyancy
-any air pockets in your wetsuit would do the same
-your lungs would decrease to about 60% of their initial volume
-because of adiabatic heating due to compression, the air in your lungs would heat up from 98.6 to about 221F; this could be injurious, possibly fatal
-your eardrums would be severely stressed, possibly ruptured (during ordinary SCUBA dives, you descend SLOWLY, in part to give you a chance to equalize the pressure in your inner ear).
Things get worse from there if the tank is decelerated at a higher rate.
If you were inside an air-filled, neutrally-buoyant bathysphere, your eardrums and lungs would be fine - but then your body would feel the same crashing impact that the water tank feels when it hits the ground.
Getting enough air into water to drop its density by that much doesn’t seem like it would be impossible. You just need to bubble a s**tload of air through it. In fact, if you hook your pond bubbler up to a series of jet engines or continuously exploding hydrogen bombs or something and drop it into a hundred meters of water, wouldn’t the bubbles expand on their way up, creating a nice density gradient decreasing from the bottom to the top? That should give you a nice constant deceleration rather than a major spike.
Aren’t you supposed to squeeze shut your asshole? (This is a serious question for feet first jumps.)
sewage/wastewater treatment plants aerate the water. We had a short channel that was about 50% air, a seething mass. Apparently it is fatal to fall into as the low density means you hit the bottom and cant swim back up. It was about 20-30 feet deep.
Of course the other option is to do it in a kayak (seriously impressive YouTube video linked).
That water under the falls must be pretty aerated (as well as having vast amounts of water pouring down into it), but (spoiler alert! 
) the guy managed to pop up again.
I always thought that with the correct technique, you could fall into water at terminal velocity and not get injured. How do cliff divers know how high they can jump from, then?