I'm right-handed and I shoot right, making me an anomaly: most right-handed Canadian hockey players who started playing at a young age shoot left. But in California, where many players picked up hockey much later in life, most right-handed people shoot right. I've never quite understood why you'd want your strong hand on the top of your stick instead of low-down to put the power into your shot, but obviously it works. NHL players are overwhelmingly left-handed shots:

Wingers are, for obvious reasons, tilted to each extreme: 41% of all right-handed shots are right wingers. And there is definitely a lack of right-handed defensemen: overall, forwards are 23% more likely to shoot right than D. Hence continued employment for Craig Rivet.

I wondered if there was any bias towards left- or right-handed shooting based on national origin:

Canada, the US and the Czechs are much more likely to shoot right, while Sweden, Finland and the former Soviet Union are dominated by left shots.