Haven't hit anything on the bikes (knock on wood), but lots of close calls with cats, dogs, deer, birds, rabbits, and yes even turtles as well
Oddest close calls I had: One time I was heading to work following a car. I notice it go over something and it's spinning around on the road after it went over it. Begin picking out a spot to swerve and avoid it when I realize it's a kitten. All spreadeagled and doing 360s along the road. Managed to miss the little guy and turned around to see if it was ok. Was small enough that the car didn't actually hit him. Just sent it for one hell of a ride.
Another time I was out riding on some country roads. Get up behind this old Ford Aerostar van, the kind with that short and really slanty nose. Just getting ready to pass him and all of a sudden there's an explosion of feathers. Next thing I see is this chicken cartwheeling through the air. It was up high enough that it looked like the guy had thrown it out his window. I'm guessing the chicken had tried, in vain, to make a last ditch jump to get out of the way. Unfortunately for him all it did was get him high enough to hit that slanted nose and ricochet off the window into the air.
I've had so many bugs explode on my shield that I can't understand how people keep riding without helmets. Considering the pings I've taken from bugs or God knows what else I know I would have been in a lot of pain without a lid.