i'd assume for most of middle earth animals wpould be kept for more labourus reasons, although a 'bond' might be established between owner and beast. (horses of rohan, cattle). i dont think most beings would be well off enough that they would have an animal for pleasure, as it mioght cost extra time and money. the richer(maybe elves, noble men) might have some pets as the above mentioned queen of gondor had nine cats. the rohirrim would be the closest i could think of, as they cared for there horses, not like the haradrim and mumakil. i guess other than that, manwe had eagles, morgoth and his balrogs wouldnt really count, and sauron and shelob is a bit comical to think of. the hobbits and elves there fore being less affiliated with war(on the hobbits part anyway) an being more 'elevated'(on the elves part) would be the ones. farmer maggot had dogs to help 'defend' his farm, but there is no evedince against the fact he cared for them. the 'pets' in middle earth could be an owners friend, but would alwaysed be 'used' for something.
woo i dragged that out....
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Half-baked