It's not the volt that will kills you, It's the amps.
Technically it's true, since the skin is presented as a resistance, so the higher the voltage, the higher the current.
But there's more:
If you measure your skin resistance with a DMM, you'll get something in the area of 100K-1M. But that's
at low DC voltage (~4V, like someone else said). A very important thing to understand is that
inner body resistance is 300-1K, but skin resistance is comparatively high (1K-100K). Since current goes through the skin, then body, then skin again to exit, measured resistance is twice the skin resistance + inner body resistance. As an example, touch both a battery's terminals with your tongue - it stings. It doesn't sting though when touching it with your fingers(skin).
Also, skin resistance drops when wet (obvious) and burnt (not so obvious). So High voltage electrocution is a cascading effect.
On top of that, skin acts somewhat like a non-ideal capacitor:mains wire(conductive) -- skin (dielectric) -- inner body (conductive). It nas no (negative) effect on DC, but some AC passes through, therefore AC electrocution is worse.
Furthermore, the skin dielectric breakdown takes place at high voltages (400-600V), so thins really get nasty.
And it's also a good idea to note that 220V mains is RMS voltage, meaning a sinewave with 220*1.41=310V peak, therefore a Peak-to-Peak value of 620V. Taking all the above into consideration, the equivalent skin resistance in AC mains electrocution is somewhere way below 1K.
To sum it all, the current requred to kill a person in less than 1mA TO THE HEART, so the closer to it you pass a current, the worst it is. Higher voltage AC exponentially increases current.
So yes, it's the current that kills you, but voltage creates current, so one could say the voltage kills you. Or both, or whatever.