Occasionally I hear about Australian players switching to the NFL, but haven't heard about it happening with other countries.
Is Australia the main source of people who have been successfull in their own country, and then switched to the NFL?
Pro-Football-Reference.com has a list of of players by country of birth. According to the list, Canada is the top place with 92 players in history, 6 active players. Next is Germany with 69 and 5; American Samoa is third with 29 and 3. Australia has 7 players listed in history and 1 as active (Mat McBriar, born in Melbourne, punter of San Diego Charges in 2014).
Unfortunately in the page is not clear how far in the past goes the number of players "in history" and "active" looks like refers to 2014 season.
Not the most one, but one of the most important
I do not know update statistics on it but in 2010 and 2011 Australia seems one of the most born-Country for foreing NFL players, but it seems there are also many other Country that offers players to NFL.
Aslo this top 10 shows: England (1) - Liberia (1) - Estonia (1) - Poland (1)- Japan (1) - Germany (2) - Ghana (1) - Tonga (1) - Canada (1) as born-Country of NFL players