How much pressure can the human body tolerate before living is impossible (e.g. skin begins to rupture, etc.)?
The answers are found in the SCUBA diving world. Diving is interesting in this sense in that 10m is roughly an increase in pressure of 1atm.
In general, you wont see humans doing well above 30atm. 300m is a "holy grail" of sorts for deep diving. Only a handful of people have ever gone that far down. And by a handful, I mean it's been done seven times, total.
NCBI provides a short paper with a theoretical limit of 1000m for humans, based on data we have collected from saturation divers to date. That would be 100atm of pressure.
Somewhere in between is the claimed record for deep diving which is roughly 600m.
Slightly higher than that, we find synthetic testing of Hydreliox. This was done in a chamber compressed to a simulated 700m (70atm). It was found that there were issues with hydrogen narcosis at depths below 500m, no matter how they tweaked the mix.
I cannot find the link, but I came across a fascinating link months ago which described the different gases you can breathe and how deep you can go. At somewhere in the 40m range, you start suffering from nitrogen narcosis, so its beneficial to use a mix without nitrogen to go lower, such as heliox. However, at extreme depths, you start running into helium toxicity issues, and adding a little nitrogen in helps with that. Yes, I said helium toxicity. At high enough pressures, the noble gasses start to kill us, and of the noble gasses, we use helium at those depths because it kills us the least!
How much pressure can the human body tolerate before living is impossible
The maximum tolerated pressure by a diver. It can be over 65 atm or bars. See: Saturation_diving
There does not appear to be a maximum pressure. We hit a limit as Cort Ammon says but that is a matter of what we can breathe, not an actual pressure limit. You get poisoned by going too deep, not crushed or torn apart.
Note that this does not preclude a hypothetical liquid breathing system. While we do not know how to build something yet (there are liquids that can carry enough oxygen and are non-toxic. The problem is it would take too much effort for our lungs to move it in and out) this is a technological limit, not a theoretical limit.