Short of collision, can gravity itself kill you? Imagine that you are falling into object with huge gravity (i.e. black hole) that does not have any atmosphere.
The question is - before you hit the ground, can the gravity itself (which would be extremely huge) kill you? And if so, how exactly that could be done? All parts of your body are affected same and in the same direction, therefore it cant tear you apart.
The "zero gravity" is simulated on earth with falling plane with speed increasing by gravitational acceleration, but is it "real" zero gravity, or is it little different?
 A: Yes gravity can kill you because as you approach something super dense like a black hole, the gravity will change with the square of the distance which means that eventually the gravity at your feet would become significantly larger than at your head. This gravitational gradient is referred to as tidal forces and is the same effect that keeps the same side of the moon facing the earth.
This would tear you up and eventually disassemble the matter that makes you. Although it sounds dumb, scientists actually call this spaghettification as the CuriousOne has already mentioned. 
It is questionable whether other effects like gravitational blue shift would not kill you prior to the spaghettification of your body.
A uniform gravitational field (which is actually only hypothetical) would have no effect comparable to spaghettification as it merely results in constant acceleration of your body.
A: While a sufficient difference in gravity over your body will kill you, gravity itself will not kill you.
It's not really clear if you're asking about hypothetical, relatively uniform gravity fields, or black holes. Since the other answers tackle the latter I'll go for the former.
Answering what I interpret to be your question, given the following ideal assumptions:


*

*You are in an extremely strong, homogeneous gravitational field (same forces acting on your entire body).

*The field is infinite in size and there is no "ground" or other objects to collide with.

*None of the other conditions present can kill you (e.g. you are magically able to survive with no atmosphere).


You will experience only an ongoing acceleration due to the effects of this gravitational field.
Density and mass do not affect gravitational acceleration. Even though your body is of non-uniform density, it does not matter, so all parts of your body will accelerate uniformly in this hypothetical homogeneous gravitational field.
You will simply move faster and faster, approaching the speed of light, but no harm will come to you. You will feel "weightless" and you will observe any stationary objects moving past you faster and faster.
You don't need the field to be homogeneous to survive either. It only needs to be "homogeneous enough" so that the tidal forces don't exceed your body's structural strength.
Now if you throw yourself in a black hole, that's another matter entirely. As already described in other answers, the difference in gravity over your body will cause the parts of your body to accelerate at different rates, and these forces tear you apart when the structure of your body can no longer withstand the forces. The cause of death here is the force that the parts of your body exert on each other due to their relative motions, as some parts begin moving faster than others.
Of course, these conditions don't really exist, but it's hypothetical, like your massless ropes and frictionless pulleys. 
A: Yes, it can.
Before going ahead, I would like to say that I am no expert with these kind of matters, so I'll be going to quote some lines which I have seen in a few videos. I highly recommend you to watch these video links which I have added at the last line, because I think that it can answer your question.

"The mass of a black hole is so concentrated at some point, even tiny
  distances of a few centimeters would mean that gravity acts with
  millions of times more force on different parts of your body. Your
  cells get torn apart as your body stretches more and more, until
  you're a hot stream of plasma one atom wide."

So as a result, you will die for sure. And also this:

"A black hole with a diameter of a nickel would be slightly more
  massive than that earth. It would have a surface gravity billion
  billion times greater than a planet that currently does. Its tidal
  forces on you would be so strong that they'd rip your individual cells
  apart. The black hole would consume you before you even realized
  what's happening."

Links:


*

*Black Holes Explained – From Birth to Death

*What if there was a black hole in your pocket? 
A: It's fair to say that the "spaghettification" problem occurs where there's a strong enough gravitational gradient across a typical body-distance - but your question seems to ask about cases where the gravity is great - extreme, but uniform (at least in terms of human proportions/distances).
Einstein’s principle of equivalence states that, as long as there's no reference externally, any gravitational field feels much like another. So if I'm in freefall into Jupiter, or the Sun, or Phobos, or wherever, I will still feel weightless, the bowl of petunias free-falling with me will also feel and appear weightless next to me. It's only when/if I look outside of the frame of reference that I might notice any difference. For example, if I were in some high gravitational field, the rest of the universe might appear to be running very quickly, turning blue, and looking very bright indeed. 
If the field were strong enough, and the outside universe bright enough (we're talking about starlight here, so it depends on where in the universe you might be, and how bright the stars are nearby - but in cases where a strong field might exist, such as near a super-massive black hole, you might find yourself at the centre of a galaxy where, presumably, you might expect the starlight to be significantly brighter than here on Earth) The "blueshifting" of low-frequency radio-wave type photons might act as microwaves, initially heating up the body fluids, visible light would shift towards ultraviolet, perhaps causing sunburn, and as we go up the frequency spectrum, xrays and gamma rays would effectively be delivering strong doses of dangerous and harmful radiation. If this were bright and strong enough, it ought to break down the proteins and structures within your cells and potentially, reduce you to a steaming pool of jelly.
So, my advice is, wear sunscreen!
A: Gravity Wave
Many users have noted that the tidal forces generated by a gravity gradient would be capable of killing you.
$\dfrac{dg}{dx}$
On a more topical note, it should be possible to cook you (among other things) using a gravity wave.
$\dfrac{d^2g}{dx^2}$
As the wave passes through you, you will experience a stretching effect (like in spagettification) and then a compressing effect (which alternates). I would imagine that the stress this places on the chemical bonds in your body would be able to convert that energy into heat.
In order for this to occur, I suspect we would need to see two compact massive objects (like a neutron star), orbiting each other at radio frequencies or above and at point blank range.
Suffice to say you will have other problems to contend with long before you feel the gentile warming effects of the gravity wave.
A: Excluding spaghettification, other fields and radiations etc. No, it would not kill you. In that case, it is just a zero g condition. Things like pumping of heart etc. will not be impacted any different from as in zero g. I guess zero g may put you to sleep but would not kill.
A: 
Imagine that you are falling into object with huge gravity (i.e. black hole) that does not have any atmosphere. The question is - before you hit the ground, can the gravity itself (which would be extremely huge) kill you? 

The answer is yes, and not for the usual spaghettification reason mentioned by CuriousOne and Jaywalker. 

And if so, how exactly that could be done? All parts of your body are affected same and in the same direction, therefore it can't tear you apart.

Let's take a look at why you actually fall down. See Shapiro's 4th test of General Relativity along with The Deflection and Delay of Light by Ned Wright, and follow it back to the Einstein digital papers. Look at the second paragraph: 

It dates from 1920. Light doesn't curve because spacetime is curved. Einstein never said that. What he said instead is that light curves down because the speed of light is higher at a higher elevation than at a lower elevation. See Is The Speed of Light Everywhere the Same? by PhysicsFAQ editor Don Koks for more on that: "This difference in speeds is precisely that referred to above by ceiling and floor observers". Your pencil falls down for the same reason, and so do you.
Nowadays we tend to call this varying speed of light the "coordinate" speed of light, as measured by observers a very great distance away from the black hole. A falling body falls faster and faster as the "coordinate" speed of light reduces. The speed at which it falls is directly related to the difference between the coordinate speed of light at the release elevation and at the lower elevation. It falls faster and faster and faster. But if this continues without limit, there would have to be some point when the falling body would be falling faster than the coordinate speed of light at that elevation. That just can't happen, because of the wave nature of matter. Or so said FriedWardt Winterberg in his 2001 paper Gamma Ray Bursters and Lorentzian Relativity: "If the balance of forces holding together elementary particles is destroyed near the event horizon, all matter would be converted into zero rest mass particles which could explain the large energy release of gamma ray bursters."
You see a mention of it this in an old Wikipedia Firewall article. It isn't in the latest article, I think there's some kind of priority dispute going on. But anyway, here's a pdf of the full paper. I think he's just got to be right. When you fall into a black hole, you don't make it to the event horizon. Instead you turn into a gamma-ray burst. It doesn't tear you apart, instead you suffer a 100% conversion from matter into energy. For a little while, your star burns bright. So it won't be you having to wear sunscreen, it's the guys watching from a safe distance! 
NB: The falling plane is a little different: gravitational potential is reducing, and gravitational time dilation is increasing. It's not quite the same as floating around in free space.  
A: My physics is much rustier than my physiology, so please correct me if I'm wrong. But as I remember it, a body in a gravity field experiences acceleration, and the acceleration is larger when the gravity field is stronger.
Well, the human body has a very small range of tolerable acceleration. The exact value depends on the direction. Wikipedia has a short section on it including photos: https://en.wikipedia.org/wiki/G-force#Human_tolerance_of_g-force, with a mention of maximum tolerance achievable after training: 

modern pilots can typically handle a sustained 9 g. 

If you are falling in the worst direction (feet first), you will already die from acceleration in the 2g - 3g range, no impact needed. You don't even need a black hole for that, Jupiter should be sufficient (25 m/s^2). The sun provides ten times that (275 m/s^2), you'll die in any direction. 
