Blue and blue-black tongues occur in several animals.
Blue-tongued skinks are named after them.
Via Bill Hughes’s Flickr photostream.
Some rattlesnakes have them.
Via The Horned Jack Lizard’s Flickr photostream.
The members of giraffidae, the okapi and the giraffe, have them.
Via djhinrich Flickr photostream.
Via zeandroid’s Flickr photostream.
And it’s one of the most notable features of the chow chow.
Via budak’s Flickr photostream.
I doubt there is a common explanation for all instance of blue tongues. The Wikipedia article on Northern Blue-Tongued Skinks says that they “have a bright blue tongue that is often used to warn off or startle predators.” While it’s clear they’re not closely related at all, it seems like a plausible explanation for the rattlesnake as well, as their “rattles” are also used to warn off predators.
It’s hard to imagine that’s true for the members of giraffidae and the chow chow though, giraffes being so tall it’s difficult to imagine any predators even seeing the tongue, and dogs usually being predators not prey. The page on giraffes on the San Diego Zoo’s website says “some people think the color is to keep the tongue from getting sunburned,” which I guess might be possible, but it doesn’t seem to explain its relative the okapi, which I imagine wouldn’t have too much risk of getting sunburns, as its short enough to get shade from tree cover, and lives in the rainforest, where there often isn’t too much sunlight that reaches the ground anyway. I wasn’t able to find an explanation for the okapi’s tongue color, most sources were more interested in the fact that they were able to lick their own ears.
I wasn’t able to find an explanation for the chow chow either, but I imagine that it’s due to human controlled breeding.
My favorite explanation for all of these tongues though is that they just eat blueberries.