The first postage stamps issued in the World are generally accepted by stamp collectors to have commenced in 1840, and this category is headed by the One Penny Black, issued by Great Britain on May 6, 1840. This is true, for the most part.
Postal systems have existed since Ancient times.
Postal cancellations came into use in the late 17th Century, and there
WERE adhesive stamps created for payment on taxed documents, prior to
1840. The unique thing about the advent of the first adhesive postage
stamps is that they were issued by governments for the "prepayment" of
postage on letters. Up until then, the letter was mailed, then the
postage fee was collected from the recipient of the letter, when it was
delivered to them.
Stamp collecting was actually born the day after the One Penny Black was issued, as many people bought examples of them, not to use as letter postage, but to save as souvenirs. Stamp collecting, as a focused hobby though, didn't really become a popular hobby until the 1860's.
The following pictures, chronological order, show the first stamps issued in the World for the prepayment of postage on letters.
Great Britain - May 6, 1840
Brazil - March 1, 1843
City Dispatch Post (U.S.) - February 1, 1842
Canton of Zurich (Switzerland) - March 1, 1843
Canton of Geneva (Switzerland) - September 30, 1843
Canton of Basel (Switzerland) - July 1, 1845
United States - July 1, 1847
Mauritius - September 21, 1847
France - January 1, 1849
Belgium - July 1, 1849
Bavaria - November 1, 1849
The first stamp issues were followed by the exponential
growth of other countries issuing stamps after 1849, and today, every
country in the World issues postage stamps.
If you would like more information on the first issues of each country in the World, the First Issues Collectors Club has an excellent website that you can visit.