If you have a kennel, you can tame most animals - not sure about buzzards specifically. If you can, you can breed them for meat or to sell to traders. For local animals, you only really need females to breed them - any wild males that come onto your map will release spores that will fertilize any females on the map, and any babies that you get from tame mothers will also be tame, regardless of the status of the father. You can also use low-value tamed animals as watchdogs, especially if you're breeding them and have a good surplus.
If they're not tameable, or if you just don't want to bother with it, you can release them in a sealed room with your military, as a training exercise. I think dropping them down a death chute gives you a butcherable corpse from untamed animals, so you might want to go that route, but check with one before you chute your whole supply - I'm pretty sure this doesn't work with tamed animals, so it might not work with wild ones either.
In either case, you can build the cages into a room somewhere and set it up as a zoo, where your dwarves can go on their breaks. This will help keep your dwarves happy. They'll also throw parties in zoos, I think, so if you're using a zoned meeting area to avoid parties, this might not be the best idea.
Personally, I tame and breed them. Untameables get piled into a cage in the corner of my animal district, and someday I'll let the military play with them.
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Topic: What do you do with your caged animals? (Read 944 times)