"It is not the voltage that kills you, it is the current" is an electricity safety tip I've heard many times.
For example, here is an experienced electrian making the claim:
The real danger with electrical shock is amperage, not voltage. Although people have been killed by as little as 120-volt AC and low volatge DC, the silent killer is the amount of amperage in milliampers that flow through a person's body.
and a claim by New Jersey State Council of Electrical Contractors Associations:
It's The Current That Kills
Offhand it would seem that a shock of 10,000 volts would be more deadly than 100 volts. But this is not so! Individuals have been electrocuted by appliances using ordinary house currents of 110 volts and by electrical apparatus in industry using as little as 42 volts direct current. The real measure of shock's intensity lies in the amount of current (amperes) forced though the body, and not the voltage. Any electrical device used on a house wiring circuit can, under certain conditions, transmit a fatal current.
and a typical forum post:
No its current thats dangerous. You can generate 20,000 volts of static electricity walking across a carpet and get zapped a littel but its not going to hurt you. Take a low voltage, High current, and good conductor path and you're dead meat.
Technically, it seems to be a correct statement. But is it any use for my safety, or is it just misleading?
I'm looking for examples of working with low voltages where you would expect to be safe, when in fact you are not. This seems to be the point of the phrase. The only example I have heard is that touching a 9V battery to your tongue is dangerous, which I think is nonsense. Luke gave a good example of burns from shorting a car battery - that's one I had not thought of.