What are the highest DC and AC voltages or currents that can be considered as safe?
The combination of 2 things can ruin your day/life: current and duration of that current. The following diagram, issued by the IEC as quoted in the body of the parent page, shows the danger zones: 




  
  AC-1 zone: Imperceptible  
  AC-2 zone: Perceptible  
  AC-3 zone :Reversible effects: muscular contraction  
  AC-4 zone: Possibility of irreversible effects  
  AC-4-1 zone: Up to 5% probability of heart fibrillation  
  AC-4-2 zone: Up to 50% probability of heart fibrillation
  AC-4-3 zone: More than 50% probability of heart fibrillation
  


However the current flowing depends on your resistance, and that depends on the contact points as much as your humidity (which conducts electricity). You'll find a table in that page among other things, and here is a copy

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Erratum: I think the last 4 cells on the right are supposed to be ohms.

[Addendum]
Interestingly (I would have said otherwise), paralysis occurs for lower currents at the line frequency (50-60Hz), as shown on the following picture (source, slide 8). It seems the human body has enough capacitance to allow more current at AC - meaning mains voltage is more dangerous than DC of same voltage as proven in this video I've just come across.


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