Just like neutrinos, it seems like NHL players prefer to shoot left. I searched on the web and found a few fans who noticed the same thing (here and here).
I'm right handed and I shoot left. When I first started playing hockey, I shot right, but the coaches made me switch to lefty. They said I stickhandled and passed better. I'm not sure if they were right (in fact, I wasn't very happy about the switch), but now I just play lefty all the time. Unfortunately, I don't have a strong upper body so I find it difficult to shoot lefty. My shot is definitely stronger with my right hand on the bottom of the stick.