Tattooing IS an option, but I don't think it holds a candle to chipping.
Tattooing is usually done on the inside of a thigh, on the inside of the lip, or on the inside of the ear, all "valuable" areas ... i.e., you couldn't remove the tattoo without doing significant damage to the appearance of the animal.
The general trend of this conversation is whether or not the chip is painful upon insertion ... it's just a needle, a single injection - like a shot. Tattooing HURTS, *many* needle pokes with dye injection, not to mention the incidence of infection. Further, WHAT would you tattoo? Your telephone number? Your SSN? What would you do if you moved and the information changed? Also, there isn't a central phone number you can call to find out what the tattooed information means. And it's unsightly ... can you imagine your baby with a tattoo'd SSN in his ear?
So yes, you CAN tattoo. The question is, WHY? Chipping is (almost) painless, is less invasive with virtually no chance of infection issues, less expensive, and has a central location for a vet to call. If you move, you simply call the sponsoring company and update your file with them: the chip doesn't need changing.
As far as I'm concerned (for whatever weight my opinion carries
) chipping is the single, most effective method to protect our furbabies.