A question that has more than one answer, as you will see.
Ether has many uses, anesthetic is one of its better uses. Fans of 'Fear and Loathing in Las Vegas' will surely remember Johnny Depp using ether as a recreational drug, although I suppose every anesthetic has been at least tried as a recreations drug by someone at some time.
Ether was first discovered by Raymundas Lullis in 1275. It only became known as ether in 1730, until then it was known as 'sweet vitriol'. (Vitriol means sulfuric acid).
Finally on March 30 1842, ether was used as a surgical anesthetic by Dr. Crawford Williamson Long. He had been using it for minor surgeries since 1842, and he didn't publish any results until 1848. Since Long didn't publish his findings till 1848, he is not given credit for being the first to use ether as an anesthetic. Dr Horace Wells tried unsuccessfully to demonstrate publicly this use of ether in 1845, and it was Dr. William T. G. Morton who is now given credit. Morton experimented on himself until September 30th 1846 at 9:00 pm; it was then that he removed a tooth from a patient painlessly. This is the first official use of ether, but as you can see not the first time it was used as such.
If you want more information about ether, and there is quite a history, check this site out:
http://www.anesthesia-nursing.com/ether.html