My aunt is a hoarder, and like Speed Racer said, it is absolutely a mental illness. The way my aunt is about her possessions, there is just no sane reasoning to it at all. She lives in squalor. She has been evicted from two homes already because they were deemed unsafe by the city (later demolished) and she's working on her third. You can't help her, she doesn't want to be helped. She doesn't have a specific thing that she hoards as she hoards everything...trash, food, items, and animals, specifically cats. She has had animal control called on her multiple times, but nothing ever happens. These cats are inbred and do nothing but multiply. There is no litterbox, so you can only imagine the filth and smell. She doesn't take them to the vet, they're just there living in filth, being sick, breeding, and dying. It's a continuous cycle.
So anyway, that's hoarding to me, as I've seen it first hand. It's sad, but the hoarder will always claim to love the animals and I'm sure they do, but they are blind to the animals' well being and appearance. I have a lot of animals, but I live on a farm so there is plenty of room to be spread out. They also all receive the care they need, the cats and dogs are neutered so no breeding. I also don't take on anything that I know that I can't afford.