A few ones I know of, not doubt there are others that occur regionally:
Cattle and pigs: tuberculosis, brucellosis, Leptospirosis, a variety of worms, liver flukes
Chickens: Cholera, Coccidiosis, Newcastle Disease, Influenza, Pox, Salmonellosis
Bees: Foulbrood Chalkbrood, Stonebrood, Small Hive Beetle,
Sheep: foot rot, blowflies, Scabby Mouth, Brucellosis, Leptospirosis, a variety of worms, liver flukes
Fish: a LOT!
Although not a parasite, animals that consume
water affected by Blue-Green Algae will become ill.
Makes you look forward to that BBQ, eh?!