I am no ornithologist, but I can say that birds do collide, because I have seen it.

As I live by the beach, there is an abundance of seagulls. If our family is eating fish and chips outside, it attracts about 30 birds on average. These clamour for attention, and then when a scrap is thrown leap into the air and often collide as they attempt to catch it. The same thing is observable at my school.

When a bird is in normal flight, however, it is very unlikely for it to collide with another bird because birds have very keen eyesight, and the volume occupied by a single bird is very small. this coupled with the large volume of useable atmosphere means that even blind birds would not hit each other often, even though they would bounce off the ground at an alarming rate!