I love them. For me, fatfurs are big, huggable teddy bears. They not only let you hug them, but they may also let you use them as a bed. But fatfurs are also giant damage sponges. They are impervious to punches, blades, even bullets, and they can just laugh off these things.
...At the same time, I have a certain style I like. I tend to like less detailed fatfurs, though I like a few details sometimes. I don't like deformed blobs or characters that look incapable of functioning.