There is much evidence to suggest that animals have their own personalities, as humans do.  For example, some octopi are happy to eat out in the open whereas others prefer to camouflage in a den to eat in private.

Parrots have a reputation for taking strong likes and dislikes to certain people.  One method parrot trainers use to gain a parrot's trust and gratitude is to arrange to rescue him from a frightening situation.

One Victorian at Rangoon made this comment on the working elephants at Rangoon, 'there are willing workers and there are skulkers; there are gentle tempers and there are others as dour as a door-nail.  Some of them will drag a log two tons in weight without a grain; while others, who are equally powerful but less willing, will make a dreadful fuss over a stick that is, comparatively speaking, nothing.'

Richard W. Wrangham, wrote of a chimp called Kakama who made a ground nest for an unrelated one year old chimp, carry it to her and lay her down in it.  He's also been seen to softly embrace unrelated baby chimps for up to an hour.  When there's no babies for him to look after he's been seen to get a log, carry it round with him and make nests for it!

 

Snakes are known to vary in personality.  Out of litters, some are more prone to show body flattening, striking or fleeing than others.  Many owners also try to train their snakes so they're not aggressive; this too varies in success according to the personality of the snake.