Least painful way to die
The American Veterinary Medical Association (AVMA) has thought about humane methods of euthanasia quite a bit and has an extensive (102 p. PDF) set of guidelines for the euthanasia of animals. The guidelines are not the same for all animals. Some examples:

Companion animals (e.g., dogs and cats): injected barbiturates are recommended

Laboratory animals (e.g., mice and rats): injected barbiturates are acceptable as are inhaled agents (isoflurane, carbon dioxide).

As for humans, you might look into the physician assisted suicide literature. I think that these generally use a sequence of drugs. As far as natural deaths, kidney failure is supposed to not be very painful.