One of my favourite modern children's authors - whom I only discovered when my sons were small - is Dick King-Smith. Most of his books are about animals endowed with rather human characteristics, and are full of gentle humour and great characterisation.
One of my favourites, which I found lying around and picked up to re-read, is 'The Sheep-Pig'. It's the story of Babe, a highly intelligent piglet who has ambitions to be a sheepdog. He is a remarkably diplomatic and polite pig, who treats sheep with respect and thus is as successful - if not more so - than most sheepdogs.
A lovely story with some humour, excitement and tension, and (of course) a happy ending. Highly recommended to read aloud to younger children, or for reasonably confident readers of about six or seven.
This was made into a film: 'Babe' which is suitable for all the family, and keeps reasonably close to the book. We saw it in the cinema and all enjoyed it, although afterwards my older son, aged about eight at the time, insisted that he would never eat any 'pig meat' again. He kept to his resolution, rather to my surprise, becoming fully vegetarian in his teens.