(We take the term literally, not as a 'mind-blowing' or non - medically referred anesthetic narcotics or products.)

In Marrakech I have seen even this century on the market a barber (?) standing with a stool, pliers and a glass jar with teeth. It seemed like a nice spectacle, but turned up there came no customers. More an attraction than an extraction.

verdovingFor painful procedures have been around for centuries sought calming solutions. The first forms of general anesthesia existed primarily to liquor up someone or knock down or strangle him.
In ancient Greece they made soporific mixtures including poppy. Dioscorides prescibed in the first century BC. wine with extracts of mandrake (Mandragora) as surgical anesthetic.
The Romans used mandrake and poppy. Probably with wine.

The Incas knew the numbing and soothing effect of coca and wild tobacco. The patients were before surgery made drunk with corn beer.
Zuni Indians of New Mexico used Thorn Apple (Datura stramonium, also Jimson weed) to stun patients during surgery.

Ancient Egyptian and Assyrian doctors pressed both carotid arteries. By thus pinching off the blood supply to the brains, the patient lost consciousness for (hopefully) the duration of the operation.
To numb the pain, the Assyrians also used belladonna, cannabis and mandrake. The Egyptians opium. (1001 inventions, Jack Challoner).
In Egypt Charaka described (2nd century AD) cannabis and nightshade to sedate patients.

In the Middle Ages they tried to soften the suffering with herbal drugs like marijuana or nightshade, the juice of mandrake (scopolamine), and opium pills with a mixture of (henbane Hyoscyamus niger) (atropine) and poppy (morphine). After the Crusades opium came via the Arab world, from China to us.

Another technique was to derive the attention of the patient, for example, by stimulating with nettles, or bring him or her in to a hypnotic trance.

The stunning of the patient was more focused on the convenience of the physician rather than the comfort of the patient. Often there were a couple of burly assistants to hold the patient.

Acupuncture as a narcotic: on this I find not much good, reliable and practical information, and nothing at all to do-it - yourselfers.

An anesthetic is a substance that is numb to pain stimuli.
The dentist uses local anesthesia.
General anesthesia is called sedation.

Known examples of overall volatile agents include nitrous oxide (N2O) and ether (diethyl ether, CH3 -O- CH3), both also used since decades as a party drug. The word drug comes via the French drogue of the original Middle Dutch droge, still recognizable in drugstore.

Opium (poppy) and hemp are also used as a painkiller since long. But the seeds of poppy were unreliable and could lead to an overdose. In 1806 Friedrich W. Sertürner tried out opium at himself, so he could make a purified product that could be used safely as a pain killer.
Also, the opium derivative heroin and morphine which are strongly related thereto are used as a painkiller.

To relax muscles or numb pain were often (witches) herbs used. Almost all poisonous plants are also medicinal. Toxicity is dependent on the dose. Therefore, the used as a drug or narcotic is too risky.

List of some witch herbs (see also: http://nl.wikipedia.org/wiki/Heksenkruid_ (witches))

Mandrake (Mandragora officinarum): (especially the apples have) a narcotic and pain stilling effect that has been known since antiquity. Can cause hallucinations.
(Wood) spurge (Euphorbia amygdaloides) especially latex and seeds are highly toxic. The caustic plant sap was used for the removal of warts.
Henbane (Hyoscyamus niger) contains toxic, narcotic and psychedelic substances. The seed was with beer vinegar (as spreads or rinse) used for toothache.
Datura (Datura) extremely poisonous, psychedelic, shamans use it in rituals.
Poppy (Papaver) the dried white milky sap contains alkaloids (codeine, morphine..) the opium or opium poppy (Papaver somniferum) produces opium, poppy seeds contain no or only traces of the active substances in opiates and can be eaten safely.
Mistletoe (Viscum album, also known as Mistel)
Monkshood or wolfsbane (Aconitum vulparia): poison also pulls the skin. A few drops are sufficient to get poisoning signs. Aconite was probably used by the Gauls to prepare curare.
Fly agaric (amanita muscaria) is eaten and smoked, can cause hallucinations.
Belladonna (Atropa belladonna) is extremely toxic, touching the berries or other parts of plants can lead to poisoning and exciting visions similar to those of LSD or thorn apple.

Morphine: product invented so doctors could sleep peacefully. (Sasha Guitry)