By safe I mean safe for us when we touch a wire that is not insulated. I have heard that human body resistance is normally 50k Ohm when dry and 20K Ohm when wet. Therefore, these voltages or currents should be safe for a person who is wet. It should be considered when no insulator is present to protect the body.
The typical current to kill a healthy person is many mA.
The minimum amount that could be harmful for a person not in perfect health might be a lot less, or if the current could be directly under the skin directly to the heart it will most certainly be less. The latter is the primary reason why medical power supplies must have leakage in the \$\mu\$A range. See, for example, this, which has references to some relevant standards (which have to be purchased).
In the more general (non-medical) marketplace, you can refer (for US purposes) to UL 508A 43.1.2 which (IIRC) specifies 42.4VDC/30VAC RMS.
Something that is a bit less than the typical amount to kill a healthy person cannot be considered "safe" under all conditions. Fewer precautions are necessary for voltages less than about 20-50V given normal skin resistance, which is why 9V batteries, 12V automotive electrical systems, and 18VAC doorbell transformers don't generally kill people. It's more than enough voltage to cause enough current to kill you if applied below the skin surface, through your heart.
High voltage at limited current or limited energy is not generally a problem- a static charge in the thousands of volts typically only causes a bit of discomfort.
For most purposes, 24VDC or lower will be considered safe enough. Most (non-electric/hybrid) electrical systems are in this range, 24VDC is very common industrial controls, many laptops use a voltage a bit under 20VDC for the chargers etc.
For a real answer though, you should seek out all the regulations that apply to your situation and your jurisdiction and ensure compliance with each of the requirements.
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
. 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.
This answer is provided for your information only, simplifying a complex question - it shall not be liable for any of your actions
I remember the current to kill from AC was about 30mA (from many years ago).
I recommend reading those, as they have much more detail and precision that it makes sense for me to copy to here.
AC currents are "more dangerous" to humans because of the skin effect. DC requires higher pressure to penetrate down to your lower-impedance tissues which it can move through more freely.
Edit: The highest-voted answer considers current and duration the 2 most significant factors. The ability to let go affects the duration of the event, not the severity; an AC transmission line will kill you (and vaporize whichever part of you touched it) before you have time to even think "let go".
Regarding current/heat damage:
AC doesn't need to penetrate your skin twice and will flow easily along the surface of it. On the other hand, AC sees your skin as a much "thinner wire" than DC. Undersized wires overheat faster, further reducing their transport area, causing further overheating... AC will burn through surface flesh to get deep, while DC needs to penetrate deep before it will flow well.
As the other answers detail, if the current is not immediately fatal (BBQ), the residual nerve/cardiac/tissue damage caused by the event's duration may still be significant and fatal.
Fatal = current^2 * duration //Not a real formula
If Fatal remains constant, raising current significantly reduces duration.
As an analogue:
DC "activates" you like a FET; you either conduct or block
High chance of lengthy duration due to let-go
AC "activates" you like a BJT; 10% of extremely lethal may still be lethal
Chance of increased duration due to let-go
Electricity and humans is a confusing topic. Clearly, at one end of the range, DC from lightning is often (but not always) fatal. Fatal because lots of amps at lots of volts has gone through a body, parbroiling it from the inside. Not fatal because some combination of factors, dry skin, insulating shoes, proximity to a metal structure, dry footing, dumb luck, a stylish hat, ... has prevented all that electrical energy from doing the parbroiling.
At the other end, very small amounts of electrical energy have killed. There was a famous case of a US Navy sailor in an introductory electricity class who decide to investigate his internal resistance using a multi-meter (using a 9V battery). He stuck the probes into his thumbs, and a very small amount of current flowed through his chest, across his heart, and seems to have disrupted the rather delicate timing of the oscillator which controls heart beats. So small a current, at such low voltage, surely didn't do gross damage to tissues. But it was enough to interfere with a (too) sensitive oscillator. It's the SA node for those curious. His heart lost stable oscillation, and began fibrillation (a kind of relatively high frequency, and uncoordinated dithering / quivering), thus killing him as his circulation stopped.
So is this electrical situation (right here) dangerous or not? If it's big stuff (like lightning) it's a question better not to even attempt to answer. Anything less, a few volts from a stiff source or not, might or might not kill. Is your skin wet, is the probable path of whatever current flows across some specially vulnerable organ (eg, the heart), is there a GFI (if it's the mains) and so on? And how could you know that the path of the current will flow through your body thus, or some other way? You can't; no one can. Anyone who claims they do is not cooking with gas.
In short there is no definite, much less definitive, answer. The best advice is give up on finding a "safe" voltage or current or electrical source, and treat all electrical sources with unwavering caution.