Years ago I was part of a bemused crew called to 'Pigeon stuck on lamp post'.
Who the hell puts these calls in I'll never figure out. Anyway a couple of old ladies and an RSPCA were in attendance on our arrival, we played the game and started to pitch a ladder, as soon as the head got anywhere near the bird it flew off much to joy and amazement of the well intentioned trio of twits.
Then there was the young vet who was clearly under pressure at a horse in a ditch bound in barbed wire job. He took a nervous look at the horse and rather than sedate it for the rescue as we were expecting, stated that he would shoot it. Our IC pointed out that it had to come out of the ditch dead or alive so we'd may as well try the live version first; I still see it trotting around now.
Chased a chinchilla around a smoke-logged flat after the bottom of its cage dropped out whilst I was carrying it out to the staircase, eventually trapped the thing under my helmet and then got a rollicking for not wearing my PPE. Shame of it was that either the shock or the belting it got when I crunched my helmet down it killed the poor thing.
Then there was a buddy of mine pretending to carry out CPR on a rat for the sake of the distraught owner, absolutely hilarious.
Once got an award from the RSPCA for multiple animal rescue at a large fire on a farm, not bad seeing as I spent all night in the warmth of the Command Unit sipping tea and answering the radio.
But the best was a tropical venomous snake stuck in a length of conduit... that the owner was kind enough to bring in to the station for us to sort out!!!! Suddenly cleaning the ablutions became very popular.