Tattoos and microchips are the alternative (or additional) methods of ID.
Tattoos are only useful if they're registered with a national service (Tatto-a-pet has one, I don't know the others). Tattoos can fade, can be obscured with hair (not as much of an issue with Boxers) and can, in extreme cases, but cut out. I don't know how the registries deal with duplicate numbers/combinations. In Canada, I think every person registering tattoos has a different code of 2-3 letters they use.
Microchips are registered when they are sold, so even if you never register your pet with a national service (AKC has one with HomeAgain, and Avid has their own), the chip will be traceable back to your vet (or whoever implants the chip - in my case, I have a breeder's pack - all puppies are chipped before they leave my house, and the chips are all registered to me. I keep a file of which puppy has which chip. The owners can register with a service if they want, but if not I will be the one contacted.).
There have been some instances of microchips migrating. I believe these were in the early days of chips, and not as much of an issue anymore. Most shelters and vet's offices have scanners - the different manufacturers' scanners will not read the *numbers* on the other manufacturer's chips, but it will note that a chip is present. The variable is whether the shelter/vet's office actually scans the dog. The AKC has reported a 100% success rate with their system (which is a bit misleading, really, since all it means is that 100% of found, scanned, microchipped dogs that were registered with the AKC program were reunited with their owners....)
I have no idea how much tattoos cost (for dogs, anyway!). Microchips are usually around $30 at the vet's office. I agree with not leaving collars on dogs unless they're on leash (there's a thread about that whole issue in the archives, if you're interested). My dogs are all microchipped, they are not allowed to run loose, or to bolt out the front door. I also have a nifty sign on my fence (can also be a license plate for a show RV or truck) that states that all of our dogs are permanently identified with a microchip - to give would-be-thieves pause.