Cats are often a product of how well—or poorly—they're socialized as tiny kittens. If you've got a snuggly, cuddly, affectionate lap cat, chances are that cat received a lot of affection and love when he was a tiny kitten. The opposite is true if your cat doesn't seem to like people at all.
These are the cats that shelters spay and neuter quickly, because they're the ones most likely to be adopted. There is some disagreement about whether this is weeding friendliness by sterilizing the cats that seem predisposed to friendliness. According to an article in Discover Magazine, a small experiment showed that, in areas where spaying and neutering rates were more than 98%, kittens tended to be more skittish than their counterparts in areas where spay and neuter rates were lower.
That suggests that spaying and neutering is responsible for "undomesticating" our cats. Several Petplace veterinarians list "making cats calmer" as a benefit to both spaying and neutering. Besides that, millions of cats are euthanized at shelters every year. More spaying and neutering can help a lot with that, by preventing cats from breeding.
The study itself only looked at a total of 70 cats, and hasn't been subjected to peer-review, which is the gold standard of scientific research. John Bradshaw, the anthrozoologist who conducted the study, also said that he's not suggesting returning to the days when most cats freely mated, since that's responsible for feral cat problems to begin with.
Bradshaw thinks the best way to control feral cat populations in cities is to address food. The less food there is, the fewer cats there will be. The problem with this, however, is that even where it's against the law to feed stray animals, people will do it anyway. Plus cats raid dumpsters and garbage cans, and are able to tear into bags and packaging with their teeth and claws.
Other experts weighed in, saying that very few genes are linked to behavior in domestic felines. In fact, socialized cats and feral cats can't be distinguished genetically from one another. So there's no actual gene for behavior.
Your best bet, if you would like a very friendly lap cat, is to adopt one that's very friendly already, or adopt a kitten and make sure it gets lots of handling, love and affection from different people so it grows up comfortable with people. And continue to spay and neuter. You're not likely breeding friendliness out of cats by having your friendly cats fixed.