I was given this warning recently in my Electronics Fundamental classes. Very safety conscious school, and in the US Navy
urban legends abound.
The basic warning: Unless you really want a Darwin award (our school, best and brightest the Navy has to offer, produces an unfair share), should you desire to measure your bodies resistance do so on the OUTSIDE of your skin. With the legend that once upon a time, a prior student killed himself (intentionally?) by stabbing his wrists with the Fluke 77 leads.
So I went ahead and looked up a functional block diagram of the Fluke 77 III (conveniently available on the web site...). The function for measuring resistance uses two paired transistors to regulate input voltage to between 7 and 9 volts. Thus, at e-troon's suggestion of 1Kohm blood resistance, our Fluke would put a current of no more than 9mA through the heart. Could probably cause a flutter, severe discomfort, and mild symptoms of electrical shock. But unless there was some preexisting medical condition it would not cause death.
That being said... I can think of a few ways to kill yourself while using a multimeter. If for instance you try to measure an excessively high voltage with a standard meter... say, 4400 volt 3-phase AC... you will likely die. But then the meter has little to do with that.
Alternately, if you trust a meter with your life and lose, ie, ignore low battery warning, you can kill yourself. My favorite though, give your lab partner the wrong values, get both rolled back in school, and wait for him to kill you the old fashioned way.