A study at the university of Missouri has determined how long ago cats were domesticated. Leslie Lyons, a feline geneticist, has studied about 200 gene markers in cats from around the world to help pinpoint this domestication. One of these gene markers was microsatellites, which are quickly mutating.
For a lot of other domesticated species, it seems that they have had multiple domestication events over the years, while cats seem to have been domesticated once, about 10,000 years ago, as humans began to migrate. When humans began to migrate, it seems they felt the need to bring cats with them, which I can't blame them for.
Cats are also referred to as "semi domesticated" because although cats do well in human care, if they were let outside on their own, they could fend for themselves and hunt just fine.