According to LDS (Mormon) theology, is friendship eternal? I am familiar with the doctrine of the sealing power, which "refers to the marriage of a husband and wife and to the joining together of children and parents in relationships that are to endure forever." (Encyclopedia of Mormonism)

It's obvious that family relationships will endure beyond the grave, however what about deep friendships? There are those who might even consider certain friendships to be as strong as family ties. What is the official position of the Church regarding whether these also "are to endure forever"? 

The larger meta-question is "what is the nature of the celestial society?" What kind of associations will there be among those who aren't sealed to each other as opposed to those who are? If there isn't a statement addressing this directly, what can be reasonably inferred from existing statements and doctrine?
There's no official doctrinal statement on eternal friendship that I'm aware of.  However, there is something that can be reasonably inferred from doctrine.  In the Doctrine and Covenants, section 130, we read:


  1 When the Savior shall appear we shall see him as he is. We shall see that he is a man like ourselves.
  
  2 And that same sociality which exists among us here will exist among us there, only it will be coupled with eternal glory, which glory we do not now enjoy.


This tells us that the Afterlife is not intended to be some alien experience that would render the concept of "mortal life as a preparatory state" meaningless, but that it will be a truly familiar thing, organized around the same social structures that we know in this life.  For that concept to be valid, it is reasonable to infer that it would have to include friends as well as family.

People are sealed to their families because family bonds are formal and eternal, but friendships are a much more informal and loosely-defined thing.  (You can probably name two people, both of whom you would call "a friend," but with whom you have two very different types of relationship.  And likewise, you have people who became your friend long after you first met them, or who stopped being your friend.  But a brother or a sister is always your brother or your sister.)  So it's reasonable to assume that, within celestial society, we will have the same inherent freedom of association with people that we have no formal relationship with as we do in mortality.