1.
birds (also rabbits, traditionally)
A counter for birds. Rabbits were traditionally counted with it too, though 匹 is now more usual for them.
Counting patterns
Note the sound changes: ば after ん, ぱ after っ.
Etymology
The origin of counting rabbits with 羽 is traditionally attributed to Buddhist monks: since eating meat was forbidden, they classified rabbits as "birds" (鳥) so they could eat them. While this folk etymology is well known, the actual origin is debated.
Usage
Used for all types of birds, from small songbirds to large birds like cranes. Rabbits are traditionally counted with 羽 too, but 匹 is now more common for them; other small mammals always take 匹.