Mr. Snuggles isn't a real cat, but an app for the iPhone.
I'm about to head off to Afghanistan for six months and will be feline-less during that time. I was looking for some kind of purr simulator and ran across Mr. Snuggles. I tell you what... For a simulated purr, it's just as soothing as the real thing.
The obvious drawback is that you don't get the tactile enjoyment you normally get from stroking a real cat's fur. But the simulated fur does react to your touch, so you can smooth it out or ruffle it up. One obvious plus is that you don't have to worry about cleaning a litter box.
Even though the app is designed for the iPhone, it works just as well on the iPad. With the "2x" feature, you have an even bigger kitty to pet.