It's hard to believe that in the early 1970s, over 95% of NHL players were Canadian in origin. This figure has been on the decline for the past 40+ years, and by 2015-16, the majority of NHL players were not of Canadian origin. It seemed to begin to change when the WHA Winnipeg Jets imported several Scandinavians to their roster for the 1974-75 season. Once the Jets became the top team for the remainder of the WHA, it paved the way for Swedes and Finns to cross the Atlantic, and make a living in the NHL.
Coincidentally, there was a hockey boom in the United States, after the 1980 Olympic Games saw the Americans shock the world to win the Gold medal. The number of American players increased from 11% to 17% in one decade since the Miracle in Lake Placid. The fall of the Iron Curtain gave way to talent from the former Soviet Union, and some satellite countries, particular the former Czechoslovakia.
As of the 2017-18 season, the composition of the NHL is as follows:
United States 27.3%
Czech Republic 3.8%
NHL Totals by Nationality ‑ 2017-2018 Stats
Interestingly, it seems that players from the former Iron Curtain seemed to peak around 2000, and has been in decline since (possibly due to the KHL). Scandinavia, the USA, and other European countries (especially Switzerland) continue to see more and more players compete in the NHL.