I actually caught a seagull while fishing once. Was pretty funny.
I was fishing with an absurdly large piece of squid, and unsurprisingly not catching anything. So I started to pull in my line quickly, watching the bit of squid skip across the water. Then a seagull thought the squid would make an easy meal, boy was s/he mistaken.
Somehow, the hook of the line got caught on the poor thing's foot. I wasn't going to let go of my fishing pole, and I figured the line would just snap as it flew away. No such luck, I had to pull in the seagull while it was flying away to the dock. Then my brother threw a towel over it to calm it down a bit (Thank you, Animal Planet). We managed to get the hook off of its foot and it flew away, probably with a phobia of squid but otherwise unharmed.
Remains the largest thing I've ever caught while fishing though.