My first thought is that it’s a way for them to identify each other, but why the butt? My dog doesn’t have to smell my butt to know that it’s me. A dog doesn’t sniff any other animal’s butt.
Easy answer: It’s the dog’s equivalent of thinking “Check out the rack on that babe”.
More complex answer (since they do this with the same gender): There are glands around there that provide info on gender, age ASF. Check out how a male reacts reacts around another male that’s been fixed. It’s all about sex and hierarchy.
Beautiful answer! I’m just posting to express amusement at the fact that The Gaspode was the source of the information. 
I think a better question is why don’t humans sniff each other’s butts?
This could explain my lack of success with women.
My dog smells EVERYONE’s ass. And their crotch. I gave up being embarrassed over it long ago.
Yeah, humans do it too.
My son, a semi-pro bodybuilder, and my future son-in-law, a professional bodybuilder, were a sight to behold when they first met, face to face.
There was a lot of posturing, a lot of flexing, a huge ‘mano y mano’ encounter.
My daughter floored me with laughter when she sarcastically said…’Look at these two, sniffing each others butt’.
Same reason they lick their balls. Because they CAN!
Au contraire! Just today, my hairless terrier went up and sniffed my cat Othello’s butt. Pissed Othello off to no end.
And I’ve had a friend’s German Shepherd constantly poking me in the lower butt when I wasn’t looking.
The reason my dogs don’t poke me: they’re too short!
If you’ve noticed the sniffing, you have probably also noticed that often a dog’s tail doesn’t really ‘match’ its body.
The reason dogs sniff each others tails is that long ago there was a large dog convention downtown. During the Polka contest (a perinneal dog favorite), a fire broke out. All the dogs ran from the ballroom, but grabbed the first tail they could get their paws on. To this day, when two dogs meet, they check each other looking for their own lost tail.
OOps- shoulda checked AFG’s link first.
How does an intact male react to a neutered male?
It’s a shepherd thing from my experience… I have a Dutch Shepherd and she does this… I’ve now nicknamed her “Mother Goose”. 
My roommate also had a shepherd of some sort, and she used to exhibit the same behaviour (the dog, not the roommate).
…and at the risk of sending this into realms some folks would rather not go, I’d like to propose that some female humans have, er…smells, that are either more or less pleasant and/or attractive, and that sometimes influences future dating behaviors by either attracting or repelling continued togetherness. It may also be true in reverse, too. THAT far, I haven’t gone. xo, C.
Before this becomes too hijacked… yes for some reasons dogs love women and their “unmentionables”. Sheba used to eat tampons/maxi pads and underware. But she only did so when left alone… so it was more of an isolation/abandonment issue than anything.
Sorry, I should have posted:
The dog loves her because she is the owner, so she acts out. She does the same thing when I go away. When I used to have to go into my job, Sheba would break into my office and eat something. (I had small toys people gave me as gifts)
Or even when I was home working, she would scratch on the door for attention.