Big Fish Games said today its users have downloaded more than 1 billion copies of its casual games from its web portal.

That’s a pretty big achievement, underscoring the growth of the market for simple but fun games which appeal to wider audiences than the traditional gaming business. The category generated an estimated $2.75 billion in worldwide revenue in 2009, according to the Casual Games Association. Seattle-based Big Fish was founded in 2002 and it claims to have the largest casual game subscription business for its catalog of more than 2,500 casual games. Those games are available on the PC, Mac, iPhone, iPad, Facebook, and Nintendo DS.

Jeremy Lewis, chief executive of Big Fish Games, said that the company is doubling its number of foreign-language sites, adding new games on new platforms and expanding its distribution channels. Big Fish raised $83 million in a first institutional round of funding in September, 2008, from Balderton Capital and General Catalyst Partners. Popular titles include Flux Family Secrets: The Rabbit Hole, Dream Chronicles: The Book of Air, and Golden Trails: The New Western Rush. Rivals include Electronic Arts’ and Real Networks’ GameHouse division.