Maybe I'm just easily impressed, but I think it's remarkable that a rooster & a hen, both with backwards-facing parts, can get those parts to touch, even briefly, while both birds are facing the same way. I can see why the roo will want to crow with triumph after a successful transaction, while the hen just ruffles her feathers back in place with a smug smile that says "I know that I'm fearfully & wonderfully made." I think she can store the roo's seed for 10-14 days afterwards to produce fertile eggs.
Some species of male birds do have penises, I think most waterbirds do, ones that mate in the water like ducks & geese. That way they can get the seed inside the hen without the water washing it away. There are other birds that do too, I think ostriches are one, but I don't want to think too much about that.
Some birds, I think mostly raptors, can mate while in the air! They fly up really high and grab each other's feet, conducting their transaction while tumbling towards the ground.
And there are some breeds of domestic turkeys that must be artificially inseminated since their body shape now prohibits natural mating.
Isn't nature fascinating?