Is it possible to kill a human with a powerful magnet? I'm asking in terms of physics. Can powerful magnetic induction rearrange spins of my body in such way I will die? How? 
Or maybe it can rip all iron from me, which would make my blood cells useless? How many teslas should such magnet have? Are there other ways to kill people with magnetic induction only? 
 A: Yes it is most definitely possible, although the field strengths needed are very high.
The basic mechanism is that a strong magnetic field alters the Hamiltonian that defines atomic and molecular electron orbitals. Simply put: a strong classical magnetic field makes the Hamiltonian anisotropic so that it depends on spatial direction (i.e. relative to the ambient strong classical field) and this radically alters chemical bond energies. It should not be too hard to see that this anistropy would wreak havoc with the reaction dynamics of the chemical processes that are essential to life.
It is estimated that the magnetic field of a Magnetar would be lethal to human life at distances up to $1000\ \mathrm{km}$ from the star. But the statistics of these lethal fields are mind boggling: for instance, the energy density $\frac{1}{2} \mu_0\,H^2$ (the $T_{0\,0}$ term in the stress energy tensor) would be ten thousand times the total energy density of lead! That is, it would be equivalent to about one hundred thousand tonnes of matter per cubic meter! From the Wikipedia article:

Magnetars are characterized by their extremely powerful magnetic fields of $10^8$ to $10^{11}$ tesla. These magnetic fields are hundreds of millions of times stronger than any man-made magnet, and quadrillions of times more powerful than the field surrounding Earth. Earth has a geomagnetic field of 30–60 microteslas, and a neodymium-based, rare-earth magnet has a field of about 1.25 tesla, with a magnetic energy density of $4.0\times10^5\ \mathrm{J/m^3}$. A magnetar's $10^{10}$ tesla field, by contrast, has an energy density of $4.0\times10^{25}\ \mathrm{J/m^3}$, with an $E/c^2$ mass density ${>}10^4$ times that of lead. The magnetic field of a magnetar would be lethal even at a distance of $1000\ \mathrm{km}$ due to the strong magnetic field distorting the electron clouds of the subject's constituent atoms, rendering the chemistry of life impossible....

At a more Earthly level: high magnetic fields of hundreds of millitesla (i.e. a few tenths of a tesla) can be lethal to people with certain kinds of prostheses. These days prostheses wherever possible are made of non ferromagnetic material but in the past there have been deaths of people e.g. imaged by NMR machines with early, ferromagnetic pacemakers, or with ferromagnetic clips in the brain to shore up vascular aneurysms there.
A: I don't know much about the topic, but here are some research points you can get started with.
For strong magnetic fields, the most notable effect seems to be visual effects (source), called phosphenes (magnetophosphenes in the specific case of magnetic causes) caused by inductance of electric currents in the retina (source).
"Studies" seem to have suggested that 50T fields cause tissue damage, for unspecified reasons (weak source). I could not locate these studies. However, the implication is that immediate death / severe damage is not caused at even 50T fields (for reference, MRIs generally run in the 1.5-3T range).
There are related questions here:


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*Effects of a very large magnetic field on the human body

*How strong of magnetic field would noticibly attract a person?
There is an interesting discussion on Reddit:


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*http://www.reddit.com/r/askscience/comments/1asgy5/can_you_die_from_a_magnet_how_strong_does_it_have/
There is also a field of study called bioelectromagnetics dedicated to biological effects of magnetic fields, which can serve as a good starting point for research:


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*http://en.wikipedia.org/wiki/Bioelectromagnetics
"Transcranial magnetic stimulation", referenced in both the Reddit and Wikipedia pages, uses small fields in the range 1-10mT to affect the polarization of neurons in the brain.
It seems that the pattern of change of a magnetic field has a more pronounced effect than the strength of the field. Static fields do significantly less (or no) damage, while at high frequencies a weak magnetic field could certainly do significant damage, e.g. a microwave oven.
Primary causes of damage from non-static fields mostly seem to be due to heat, or due to induced electrical current; for example, from the ReviseMRI link above:

A more serious consequence of electric currents flowing through the
  body is ventricular fibrillation (though these levels are strictly
  prevented in MRI). ... As a general guide, the
  faster the imaging or spectroscopy sequence, the greater the rate of
  change of the gradient fields used, and the resultant current density
  induced in the tissue is higher.

It would doubtless take an extremely strong magnet, higher than anything we could produce, to pull the iron out of your body (conjecture, no source). Note also that there is only about 3-5 grams of iron (something like 2 cm3) in the human body (source, unreferenced source), mostly bound to hemoglobin.
Count Iblis pointed out, in question comments, that there is a nice discussion of magnetars and strong magnetic fields here, which provides nice overviews and plenty of interesting information  (although a bit dated):


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*http://solomon.as.utexas.edu/magnetar.html
From there: 

Fields in excess of 109 Gauss, however, would be instantly lethal.
  Such fields strongly distort atoms, compressing atomic electron clouds
  into cigar shapes, with the long axis aligned with the field, thus
  rendering the chemistry of life impossible. A magnetar within 1000
  kilometers would thus kill you via pure static magnetism -- if it
  didn't already get you with X-rays, gamma rays, high energy particles,
  extreme gravity, bursts and flares...

As for long term effects of more commonly encountered field strengths, there is generally little association between magnetic fields and cancer (source, source).
I hope this helps. Sorry I do not know a direct answer. It certainly depends on more than just the field strength, however.
A: I'll answer more in a clinical perspective. I don't know about extreme situations when the spins of your organism's atoms are rearranged in a lethal way, but as far as MRI magnets go, the first concern when using MRI equipment is the possible induction of electric currents inside the human body.
These concerns are more prevalent for investigation MRI magnets, which are more powerful than the ones typically used at an hospital (they go up to 3 Tesla, while the ones used in academic research can go up to 9 Tesla. Record-breaking magnets reach 11 Tesla).
The human body starts to suffer from current induction when the exterior magnetic field reaches around 7 to 8 Tesla. Symptoms include increase in body temperature, diminishing brain functions and even hallucinations (never witnessed this one, but I've heard it's possible. Still, take this last symptom with a grain of salt). All this considering patients don't have metallic implants, obviously, or exposure can be lethal. The "Specific Absorption Ratio" is commonly used to try to measure these changes in the human body (expressed in Watt/Kilogram).
Conclusion: Before the human body dies of "iron loss", the effects of induction can be lethal for weaker magnetic fields. MF's around 8T can have a noticeable effect in the human body.
Sources: My knowledge comes from my work and my studies, and I can't reveal them here (I'm sorry). However I cited this article for one of my projects, and I believe it sums up my point nicely:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2705217/
