The main current alternative to the World Amateur Chess Championship is the Amateur Chess Organization (ACO), most notably its recently established world championship of chess, a rival to the WACC annual tournament.
Whereas the WACC is officially recognized by FIDE (Fédération Internationale des Échecs), the ACO's annual contest is not, meaning titles or points won at any ACO event does not count towards a chessplayer's world ranking.
The first official world amateur chess championship took place alongside the Paris Olympics of 1924, with the second WACC concurrent with the 1928 Amsterdam games.
This was the final WACC until the 1997 tournament in Hastings, UK, since when the WACC has taken place annually. The 2015 WACC will take place in Chalkidiki, Greece, between April 13th and 22nd.
The ACO's world chess championship event first took place in July 2012 in Dubai, UAE and the 2014 event was held in Rhodes, Greece. 237 players took part from 26 different countries. The 2015 ACO championship is scheduled for the Greek island of Kos, May 9th to 18th.
This ACO promotional YouTube video tells you more about the WACC's new rival: