I have a German Shepherd (Akela) who doesn't chase bikes but is a bit of a danger to pedestrians. Wonderful dog for camping, though--very protective and can find her way back to camp when the person with the map and compass gets confused.
Certifiable Frisbee fanatic.
I also have a pet rat, who probably WOULD chase bikes, if he had the option. (g)Nash is my third rat, and this one has a bad Jekyll-and-Hyde personality. He's sweet and friendly most of the time, but clean out his cage and he turns into a raging berserker who would rip your fingers off.