Why on earth do dogs enjoy doing this?
The answer is simple: it's an instinct.
If your dog could talk, he probably wouldn't be able to tell you exactly why he does it, either. No one is sure what the attraction is, but there are three working hypotheses.
One is that dogs are attempting to mask their own scent. This would be a holdover from their origins as wolves. Masking their scent may help wolves sneak up on prey without alerting them by way of smell.
A second theory is that rolling in feces or a dead animal's remains is a way for a dog to communicate that he's found something interesting. The dog (or wolf) then transports that smell back to his family (his pack) in order to advertise his discovery.
A third theory comes from the book, The Truth About Dogs, by Stephen Budiansky. It is possible, Budiansky writes, that we've gotten it backwards. The dog may not be trying to absorb the scent; instead he may be trying to impart his own scent onto the object of his interest, for the same reason that a dog may urinate on a tree. The purpose may be no more than to leave a calling card - to overmark another scent.
What do you think?