Can a diver swim a short distance in great depths without being physically crushed by the pressure? I recently saw "The Abyss".
Does it make sense that they do dives in these depths (700m) with soft suits?
Also - what is all the depressurization talk about? Why do divers need to depressurize long periods after they resurface? Does that mean crew members can't escape drowning submarines?
 A: A diver's body is basically made of water, and water is incompressible to a good approximation over the relevant pressure range. So the physiological effect of the water pressure itself will be negligible: I expect there is no problem with diving at 700m in soft suits in that sense. 
However, in order for the diver to inflate her lungs, she must have air supplied at the same pressure as the surrounding water. Breathing pressurised gas brings its own set of problems. The most prominent of these is a serious class of injuries called "the bends". This is a danger because the pressure increases the solubility of nitrogen gas in the blood and tissues of the body. The concentration of nitrogen dissolved in the diver's tissues increases with the time spent at depth, as the diver breathes more and more gas. If the diver then ascends too quickly, the sudden decrease in pressure causes the nitrogen gas to come out of solution and form bubbles. Potentially this results in excruciating pain or death. 
Submarines have a rigid outer shell which allows the air inside to remain at atmospheric pressure even at great depth. So as long as the poor sailors can hold their breath all the way up, then there is pretty much no risk of the bends. More likely, submarine escapees will require some compressed air source if they are to have any chance of making it alive to the surface from the depths usually plumbed by submarines. In this case decompression illness does become an issue.
If I remember the Abyss well enough, the kind of deep diving they were doing would have required weeks and weeks of gradual decompression in a hyperbaric chamber before the return to normal surface life. The idea of trained divers forgetfully decompressing themselves by accident from 70 atmospheres to 1 atmosphere in a matter of seconds is so ridiculous that I burst out laughing every time I watch the end of that film. It's still an absolute classic, though :)
A: The other answers already treat decompression sickness, but in addition to the submarine scenario:


*

*How long would one have to hold one's breath? A good diver can apparently maintain something around 0.5 m/s (plus some Buoyancy due to the air in their lungs), so even for a Civil submarine at around 30 m depth, they'd have to hold their breath for a minute. At deeper depths, Buoyancy may have a more relevant influence since it's an acceleration, but still, holding your breath for a mere minute (plus you probably didn't get the chance for taking a deep breath before having to escape the submarine) is troublesome. And as Philip's answer mentions, you have to breath out since your lungs expand (the expansion would increase your buoyancy though). I don't know any details about that case, the Wikipedia article lacks detail, so I can't tell whether these two survivors were good swimmers or had luck...

*<<My ears! Where is "up"?>> Even at 30 m the pressure is already 4 times the atmospheric pressure. This sudden change (due to your hastened escape from the submarine) might cause your eardrums to rupture, which in turn can lead to Vertigo - you might confuse up and down and accidentally swim deeper instead of towards the surface.

A: Some of these responses are hilarious, yet some have a bit of accuracy.  For the man who asked the question... never believe anything seen on TV.  Ever.
Have divers been to depths greater than 100m, 200m?  Absolutely.  Does it require a monumental amount of time, money, planning, and training?  You bet.  Not just the decompression, but the acclimation to the pressures prior to the dive, and handling life under these pressures is also vital to the job.  It is true that most of the body is made of incompressible tissue and liquids... ie. blood, bone, muscle, interstitial fluid, inter/extracellular fluid, lymph, brain, etc etc etc...  but within all of this is dissolved gases;  nitrogen being the most abundant and is not metabolized by the body.
decompression at any depth for any amount of time is required by your body to rid of these gases properly so as not to accumulate in a part of your body and become "trapped" which can cause all sorts of ailments.  longer deep dives, Type 2 decompression sickness is most common, whereas shallow dives arterial gas embolisms are the most common.  all are severe and all are potentially deadly.  The degree to which a person may be susceptible or even affected is different for each case.
The deep diving is done by those known as "saturation divers".  This is a term given to those that dive very deep for extended periods of time.  The time at depth is so long that their body is literally completely saturated with the maximum amount of dissolved gases that can be compressed at the given depth.  Where you are currently sitting to read this is where you live within a few feet of elevation... you have been there for a long time.  You are saturated.  To go up in elevation requires off-gassing. Ever heard of altitude sickness?  Same thing for a diver who comes up form the depths, only at a much greater scale due to the pressures of water versus air.  the deep and longer under, the longer decompression required.  In-water decompression is possible, though surface decompression (SUR-D) is the preffered method due to controlling the environment.
How do I know what I am talking about?
I was also a Navy Diver myself and was stationed in Panama City where the Navy Experimental Dive Unit is located.  The two story dive chamber there is designed to crush a diver to extensive pressures equivalent to more than 700 feet of sea water.  It is the same facility where the infamous Carl Brashear (Men of Honor was made after him) made one of the deepest dives recorded.  Most of these divers suffer long term effects of diving that deep... 
A good friend of mine teaches submariners to escape a submerged vessel in emergency and how to survive.  Ho-Ho-Ho is the chant on the way up.  It is a way to steady your exhalation and let out enough air to keep your lungs from popping from the reduction in pressure as you ascend the water column (Boyles Law) and not run out of air before making it to the surface.  A submarine is further designed to make emergency surfacing possible via "chicken" switches i nthe event the vessel is compromised.
Another friend was stationed in San Diego with Consolidated Dive Unit (same guys that were cast in Men of Honor as the divers) that owns the 1 atmoshphere suit.  It is capable of making dives far deeper than anyone might think is possible.  that number is for me to know and you to only speculate...
There is much more detail to diving than just going down and coming up.  rule of thumb...  30 feet per minute on a dive that does not require decompression. If so, consult the U.S. Navy Dive Manual for which all diving is referenced.
A: The pressure itself doesn't really matter as Mark pointed out. Neither does the bends if you stay at the same pressure - it is caused by gas coming out of solution and forming bubbles as you rise (and the pressure drops)
The real challenge at very deep deaths is the chemical effects of gases at high pressure.
Normal air scuba is limited at around 40m because nitrogen at higher pressure makes you drunk. You can use air with added oxygen, ie less nitrogen, (Nitrox) but oxygen itself becomes toxic at higher pressures.
You then replace some of the oxygen and nitrogen with helium, or hydrogen - making Trimix, Heliox and Hydreliox. The problem is that at each depth you have to balance having enough oxygen to keep you alive, but a low enough concentration not to be toxic - so you need to continually adjust the mixtures and types of gas as you ascend and descend. At very large depths these limits get very tight.
The different toxic effects of helium and hydrogen aren't very well researched and can vary a lot between different people under different conditions.
The record for diving use flexible suits (as opposed to hard submarine suits) is something like 700m but the systems are so complex and expensive that it's normally easier to just use ROVs and so it's not heavily researched.
A: The compressive effect on the body itself is not a problem because we are composed of incompressible fluids and solids. All gas filled cavities in a healthy person are connected by tubes to the outside so that the internal pressure can be equalized as external pressure increases.
A deep diver is affected by a variety of other problems that can be corrected by adjusted the gas mixture.
Nitrogen is a narcotic that affects judgement as depth increases. This can become significant from 30m and is seriously dangerous from 50m down. The effect is mitigated a little by getting used to deep diving, but the sensible way to avoid nitrogen narcosis is to use a breathing mixture with less nitrogen. All gas toxicity problems are dependent on partial pressure so if you replace half the nitrogen with helium which is not toxic you can go to twice the depth without narcosis.
Oxygen is toxic with very different symptoms. It normally causes spasms and fits at 80m with probably fatal consequences. Again the remedy is to replace oxygen with helium but you need to keep enough oxygen to breath.
Despite these toxicity problems some people claim to have reached depths up to 155m on air for brief moments. It is almost suicidal to attempt anything deeper than 100m on air.
To go deeper you can use a mixture of helium and oxygen but at about 250m you start to suffer from High-pressure nervous syndrome. This is not a gas toxicity problem but a direct effect of pressure on the functioning of the nerves causing shaking. Luckily this can be corrected by adding just the right amount of nitrogen back into the gas mix. It is as if narcosis and HPNS have opposite effects that cancel each other out.
Using the right mixture of oxygen, nitrogen and helium it has been possible to go deeper. The record is unofficially 318m by Nuno Gomes in 2005. Problems are to control the gas mixture ratios as you go deeper. Off course it can take weeks to decompress allowing the gas dissolved in blood and tissue to escape slowly without blocking blood vessels or nerves. You also need to control the temperature of the gas carefully because helium at high density has a high heat capacity and hypothermia is a potential problem. The viscosity of the gas mixture also makes breathing more difficult as pressure increases.
It is likely that there are other unknown problems that would limit diving long before reaching 700m without hard suits.
Deepest escape from a submarine without scuba is probably about 65m, two survivors from HMS P32 1941. The short exposure to pressure in such circumstances means that decompression is not a serious problem but they need to breath out constantly on the way up as the gas in their lungs expands.
