Golok,
I've had cats for most of my life. They have been good for quite a lot for me.
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To begin with, the cats I've had did either chase away or kill anything smaller than themselves which entered the territory. They were very effective at clearing the area of rodents, reptiles, birds, and insects.
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My cats were also great as alarm systems, waking me and letting me know if anything odd and potentially problematic was up.
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And, yes, they really do make great foot warmers.
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As for looking lovely--I place a lot of value on their aesthetic contribution to my environment.
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My cats were also good friends. They rushed up to me and greeted me with genuine excitement and pleasure every single time I came home. They'd tag along on neighborhood walks. They preferred to be near me than anywhere else. They were very playful and loved to play with me. They'd show me stuff that interested them.
The friendship was one of the biggest benefits they gave. Perhaps you are incapable of having a real friendship with an animal. If you can find this ability within yourself, I guarantee you'll be a better person for it.
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I also learned an enormous amount from them. They reminded me of the simple life where one is content with being and doing, instead of basing happiness upon various artifices we create and impose on ourselves. They served as demonstrations of what utter joy really means, reminding me and helping me find it again in my life. They expressed pleasure from the simple presence, or touch, of a loved one, helping me come back to the eternal verities.
They also taught me the ways of animals. They taught me how to stalk wildlife. They showed me how to sit or lay comfortably on a variety of shapes and surfaces. They taught me how to shift at will from being a human in my domesticity, to being an animal among animals and nature (instead of the misplaced foreigner the most people are when put into the natural world). They taught me how to move with elegance and efficiency through the natural world. They taught me how to smell the world and learn fro what I smell, and how to listen to subtle noises and glean from them. They taught me how to be an animal whisperer.
As a professional nature photographer, I owe a large portion of my success to what I learned from observing and interacting with my cats.
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If you read the book Love and Survival, by Dr. Dean Ornish, you will see dozens of doumented medical studies of the health benefits and life-extension benefits of cat companionship. They create health benefits through giving people relaxation, distraction from stresses, love, and giving lonely elderly people touch, exercise, and purpose.
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Finally, I consider the question "Are cats good for nothing?" to be somewhat absurd, and also kind of sad. You will be a happier and better person if you come to recognize an intrinsic worth in all living organisms.
--Mike
My daughter has "her cat" along with her hamster, her rabbit, and her fish. Of course the family lab joins in and sleeps in her room known as the zoo. 
Esepcially the one we have now. He's more dog than cat. Hates cats, loves dogs.
