Once I was riding my road bike down a rural road. I heard barking over my shoulder and saw two dobermans running toward me. I can't think of a time in my life that I felt more endangered.
I reacted instinctively and accelerated. Unfortunately I was on a gravel road and going into a bit of an incline. There was no way I could outrun those dogs. I looked back over my shoulder and they were no longer chasing me. The cycling gods must have been smiling on me.
Another time, in a similar situation, a different dog ran along next to me, barking and baring its teeth. I maintained my speed and yelled at it (trying to assert some dominance) until it got tired of chasing me.
These two experiences have done a lot to put me off touring alone.
How do I deal with issues like this?