Always been curious -- it's been stated that Pokeballs are the resting place for Pokemon, but has there been any evidence to show that Pokemon are incapable of leaving their Pokeball for another Pokeball? Makes me curious if Pokemon are tied to their Pokeballs for their entire lives, or are they able to be swapped around?
Short Answer: Yes
Long Answer: There is a link, but that link can be broken
It is not possible to catch another trainer's Pokemon with an ordinary Pokeball, or any of its variants, including the Master Ball. If you try, nothing happens and the trainer basically says "Oi! You can't do that!".
In addition, when releasing a Pokemon, it is bathed in a blue light instead of the usual white light of materialisation or the red light of dematerialisation.
These two facts strongly imply that there is some link between a Pokemon and the Pokeball it resides in, once caught, and that this link can be broken by a trainer to release the Pokemon back into the wild.
However, it is possible to catch a trainer's Pokemon with Specialised Technology. This also implies that there is some link between a Pokemon and it's Pokeball that must be severed / ignored on some level in order to "snag" them.
Another example of catching trainers' Pokemon was the use of Mewtwo Balls (yes, that is their real name) in the movie Mewtwo Strikes Back. However, these particular balls not only caught Pokemon, they could steal Pokeballs as well, and after the Pokemon inside had been cloned, the Mewtwo Balls released the Pokemon they had stolen, though this returned them to their trainer, rather than actually releasing them to the wild.
With the Pokemon's cooperation, it should also be possible, in theory, to release them and catch them in another Pokeball, if you wanted to switch.
In short, a Pokemon does have a link with the Pokeball it is caught in, and it isn't possible to change that without careful planning and/or some specially made tech.