First of all, I am really glad cats don't chase bicycles either! Second, dogs, even friendly ones, are very dangerous to cyclists. Arielmoon & Mimi said it all.
The only thing I can add is that one of my best friends had an accident involving a friendly dog in June. My friend was riding his bike 8 mph (he was just topping a hill) on a quiet country road, saw the dog (off-leash) coming toward him and knew he was friendly because he also knew the owner - who also happened to be walking down the road. What he did not anticipate is that the dog was going to turn directly in front of his bike just as the two met. My friend's front wheel turned sharply to the left, he went down on the right in a slow-motion crash and broke his femoral neck. A rush to the hospital, emergency surgery & three screws later, his leg was back together. He is now concerned about avascular necrosis.
His experience has completely changed the way we react to dogs on our bikes now. In every instance, we brake hard and try to stop or ride very very slowly until we know what the dog is going to do. Fortunately for us, the dogs generally are friendly and just want to chase. Once we slow or stop they lose interest.
Be careful out there!!!
"When I'm on my bike I forget about things like age. I just have fun." Kathy Sessler
2006 Independent Fabrication Custom Ti Crown Jewel (Road, though she has been known to go just about anywhere)/Specialized Jett