The local shelters and rescue groups here chip all of the animals
before they adopt them out. Just last year, one rescue group got in a
cat that had been adopted out by another local rescue group. They
called, and the first group picked up the cat.

Microchipping is very safe. The odds of a problem are extremely small.
How often does an indoor only cat get outside? Mine don't hover by the
door or try very much, but they still manage to escape on rare
occasions. I've had Jay Jay for 5 years now, and he escaped twice in
the first year. I've had Sassy Taz for a year and a half, and she has
gotten out at least 5 times. (None of these times were because of me).
We got them back inside quickly. But it proves that it can happen.

Add in an earthquake, fire, floods, etc, and you may need that
microchip to pick up your cat from a shelter holding hundreds of
suddenly rescued pets. Most vets also have scanners, so people who
find a pet wandering can go to their local vet and have it scanned.
Collars come off. That's the whole point of a break-away collar, to
come off if it gets caught on something.

I would also point out that many horse registries have been using
microchips for over 10 years as the official method of identification.
I go to the annual friesian judging, and they don't judge a horse
until the microchip has been scanned. Foals are chipped by the
judges, and the dam is scanned for a chip. I've seen hundreds of
horses scanned, and only one chip had moved noticeably. And I have
never heard any horse owner complain about them. These are horses that
start out at $6,000 - $10,000 for a foal and only get more expensive.
They would not be doing the chips if they considered them risky.