I am a right handed person, but I try to get the left hand to do an activity the moment I am conscious about it. Two such examples are brushing teeth and using the mouse. Long time back I started using my left hand for brushing. Even 15 years later, it doesn't feel natural but I got good at the finer movements.

Around the same time, I was playing a lot of video games and got Carpal Tunnel Syndrome, so I started using the mouse with the left hand. I can't draw well with the left hand on say in MS Paint, otherwise I got pretty comfortable with it.