A quick Google shows that ~20 people per year are killed by cows per year in the US. So not very dangerous, but not super safe either (cows kill more people than sharks - although that mostly shows how few people sharks kill).
Pigs are extremely dangerous to children in all cases (they will eat body parts with no hesitation and no effort, like carrots).
Goats are incredibly awesome and accept you as part of their pack and defend you from predators. They can also be assholes but playfully. As with cows, female only herds, as males are dangerous.
I've never herded sharks so I'll go with your opinion on those.
I was able to hang out with a group of cuttlefish though. Cuttlefish are weird and cool.
"A report by two shark experts has concluded that regular feeding of the large assembly of sharks at the site had encouraged the animals to adopt “begging behaviour” that led to the fatal incident. "
It won't stop me hanging out with sharks when I get a chance (but only some species - not Tiger sharks or White sharks!).