When set to follow a multiple-waypoint route, my (Simrad) AP will change course automatically, as long as the course change doesn't exceed something like 15 degrees. It also has a follow the bottom contour mode, which can be great for fishing, in which it seems quite willing to make significant course changes without user confirmation.
As Dave mentioned... worrying.
Just as you are out on the side deck showing off the fish your AP has helped you to catch, to the friend who has come up close alongside for the viewing, the AP automatically turns 10 degrees to Port and suddenly you are in trouble.