Licky Dog

[Biciclista]

Now that i've seen the video, are you sure that there isn't steak juice on that other dog's backside? In cats social grooming is a big plus. the groomer would lick the other cat (notice the dog laying down was not complaining) until the recipient gets tired of it, but it's a way to get into the good graces of another.
I've had cats that licked themselves raw, that's a very different thing, a nervous disorder, or like bmccasland, they need a job to do, they have all this energy and nowhere to go with it.

[TsPoet]

It's interesting. When dogs lick themselves, usually the paws or legs, it's considered to be either nerves or aches. But, I've never seen a dog lick another dog like that. I still wonder, though, if it's nerves.
Murphy started licking his paws when I got Finagle over a year ago. I do find with him that I can distract him - it's a fine line, though, a playful ball or something could reinforce the behavior= When I lick Mom plays with me.
Have you tried something like a Kong? The Kong works for my mom and her Rottie - the Rottie has had several knee surgeries and she can use the Kong to distract the dog away from chewing on her knees.
http://www.kongcompany.com/worlds_best.html
I don't think that would be a permanent 100% of the time distraction, though - or you'd end up with one fat dog. Maybe occasionally put peanut butter on the kong, so it's a lick toy and reinforces the lick toy aspect of it.

[sundial]

Some dogs do develop behavior similar to OCD and their vet prescribes an Rx for this.

[OakLeaf]

Measle was a compulsive licker also, although I don't think to that extent. He'd lick people and other dogs. He did have a lick granuloma late in his life, but he'd been a licker from a puppy. I think obsessive/compulsive traits probably was it - he was VERY clingy and needy (apparently abandoned as a pup), so probably licking helped him feel like he was bonding with the lick-ee. He did tend to do it more when he was stressed.

[Zen]

I guess i'll ask the vet next time I'm there.
She is clingy (she's my living, breathing lumbar support) and very protective.

This dog has issues

[sundial]

All dogs have issues. I've had one that was unnerved by anything loud, like low battery alarm in our smoke alarm, thunder, gun shots (by the area hunters sighting in their rifles), backfire, etc. I have another one that detests anything that comes close to her ears. She hates having her ears looked at.

[greycoral]

Watch this when you get home.
She licks everything. Herself, Ginger, upholstery, chair arms...it's maddening!

Our Boston Terrier is like this too. He licks his paws all the time (he's got allergies), and will often lick our other dog like your video. I have always thought it was a submissive sort of thing, our pug (the other dog) is definitely the alpha in this house. But he does like to lick the furniture, your hands, jeans, anything!!