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!

A robin will chase another robin if his territory is invaded; many other birds engage in long twisting chases when they are courting; a merlin or sparrowhawk will doggedly follow its prey through many high-speed turns; other predators chase food-carrying birds to force them to drop their mouthful. If you see any of these chases you will be astonished at how quickly the follower can change course and how incredibly manoeuvrable they are. It's a fair bet, that with these skills, birds don't often collide.

Greedy seagulls in pursuit of junk food excepted!

I heard this from a very clever professor of pain medicine recently: he explained the process of Synaesthesia: i.e. the blurring of our senses so that a person with this condition may hear colours or see music or taste a smell or vice versa.  The theory is that birds in a flock, e.g. starlings  sense each others closeness (by eyesight) as 'touch' so know exactly where each of the birds around them are and thus do not collide with each other, despite making sudden and frequent changes of direction

A few years back now, my wife witnessed two seaguls in mid-flight, collide head-on with each other in the city area of Melbourne. They were dazed, but otherwise ok.

So yes, they do collide. But as there are not too many eyewitness reports of this type of thing happening (I have yet to see one happening as well), it therefore appears to most likely be an uncommon event.

I don't know about other birds but pigeons can see at 75 frames a second, much faster than us as TV works at 24 frames a second. This means that compared to us, they see things in slow motion and so are unlikly to collide.