This topic is very controversial to begin with. Some people probably have not even heard of pets having tattoos. However, pet tattoos happen a lot more often than one may think. For instance, race horses are given a tattoo in their lip right before their first race so the horse can be identified. This tattoo is used if for some reason the horse's records get lost in between different owner's. The new owner's can then track down the horse's records with the tattoo in their lip. This same practice is used for dogs as well.
Many dog owner's chose to get their beloved dog tattooed with a series of numbers on their belly in the event of the dog getting lost. The tattoos are sort of used for the same purpose as a micro chip. With that being said these tattoos don't seem to be very cruel. However, the tattoos are administered the same way as a humans so people may feel that in itself is cruel. But people should know that the tattooing itself doesn't hurt the dog like it does a human because they have more layers skin, but it is still uncomfortable to them. The sound of the tattoo gun is want makes them the most uncomfortable.
With that being said tattooing your pet doesn't sound so bad. However, to tattoo your pet just because you feel it would be "cool" for your pet to sport a tattoo, probably falls somewhere under animal cruelty. Getting a series of numbers tattooed on your pet is a whole lot different that getting an actual tattoo design tattooed on them.