While a dog chasing a lone cyclist will tend to stay behind or to the side of the bike, generally allowing you to keep pedaling and outrun the dog, I once had a different situation. I was pedaling with a group and the dog went for the bike ahead of me. I couldn't avoid it, hit the dog, and went down. My bike and I weren't hurt, but my wool Stil-long long underwear pants (worn under my shorts) were torn at the knee. Given that these were expensive wool long underwear and I was a poor student at the time, I actually went to the home that the dog came from and knocked on the door. My attempts to get the owner of the dog to pay for a new pair of Stil-longs were unsuccessful, and I later was able to patch them. Just a note that dog encounters don't always end as positively as Lisa's.

Then there are the country dogs that will wait for you 1/2 way up a hill...