Even smaller birds can be a threat. The overpopulation of Canada geese is an issue on trails near water. They get aggressive when they have goslings. I've been chased on numerous occasions and have had them try to block my path. I even had one land on my backpack and peck at my helmet on one occasion!
The most bizarre incident I've had though was when a grouse came out of the trailside grass and ran alongside me. I thought it was funny until he took a nick out of my calf!
It can be tough to keep your bike on the trail sometimes with all these wild foul!