This looks like a Blue Russian. I had one about a hundred years ago. he would demand that you pet him, but only three times! then he would grab your hand in his teeth and hold it there before he got up and left.
The British Shorthair, a stocky, sturdy cat resembling a plush teddy bear. While blue is the color most associated with the breed (like the one pictured), British Shorthairs are found in a number of other coats and patterns as well.