My idea of domestication is creating a new species through human contact that is beneficial to humans.
2 or 3 generations is not domesticated. I wouldn't consider anything other than 60-80 generations to be domesticated.

Cows, Pigs, Cats, Dogs, and even some Horses have been altered from their original wild ancestors, over hundreds of years for human benefit.
You wouldn't be able to find a naturally born and bred generation of black and white dairy cows in the wild that wasn't released by a human at some point. Wild pigs are VERY different from domesticated pigs.
Dogs even have a multitude of influenced breeds, when it really all originated with coyotes and wolves. (And I don't mean by colors, like with morphs, because that's genetic and can occur over one generation, while actual structure takes many more.)

When people say 'wild cats' I don't really understand. There is no such thing as 'wild house cats'. They are loose domesticated cats.

So no, I don't think snakes will ever be able to be domesticated, because we really have no benefit out of them other than pets, and even then they aren't very beneficial because they have such little intelligence.
I think parrots could be eventually, but it would take a lot of time. They are intelligent but I would think it to be harder than with mammals for some reason. I don't have any facts behind that, just a hunch.