sharke
Rain
craigb
This is because dogs are your pets. Cats just agree to live with you and let you share their space. 
I'm guessing that's also why they are more inclined not to pee and poop everywhere. Which suits me better, too. :P
Oh I don't know - I deal with a lot of cats in my line of work and I have met more than a handful who have been inclined to poop wherever they please. Cats often use their toilet functions to express anger. Like when their owners are away, they will mysteriously "miss" the litter box and start pooping just off to the side. Or the middle of the living room. We had a cat when I was a kid who, if you gave it the wrong flavor of cat food, would turn right around and pee in it before walking out of the room and licking herself arrogantly.
There are indeed problem kitties - we have one of our own. It's been a bit over two years and she's been a problem from the start, due to a combination of health issues and ensuing behaviour issues. She MIGHT stand a chance of acting a bit more normal in a house with no other cats, but I wouldn't bet on it.
And of course, some of cats are just bad apples. A friend of ours has one of those temperamental cats - though he also has health issues, so I wouldn't rule that out entirely.
That being said, in a very large part of the cases I've seen, behaviour problem has a human cause or an environmental one.
Besides that one cat I mentioned above, and another senile 18 year old cat - who had so many health issues that we had to have her euthanized - in my experience, pooping and peeing just does not happen unless there is a health issue.
Puking is a different story though - dogs can't hold a candle to cats in that department. Cats are the absolute masters at that. Ours seem to be allergic to clean floors...