I've had more encounters with animals while duck hunting, rather than fishing. Having a beaver tail slap the water while canoeing across a pond with a 90 lb lab in the boat in the black of night is an eye opening experience. I've also heard of friends having bald eagles and snowy owls swoop down and steal ducks that were just shot. One of the best encounters that I have seen/ heard of was with a seal and a duck hunting guide in Rhode Island:
http://m.youtube.com/watch?v=jyMEBNgNZNM
The coolest experience that I have had was in Montana, when I had an opportunity to fly fish while a bison casually hung out about 100 yards away on the other side of the river. I also got to see a golden eagle swoop down and grab a trout out of the river we were fishing, which was also pretty cool.