Common interests. This probably ties us closer to our friends than many would like to admit. When our interests diverge and we can find nothing to enjoy jointly, time spent together tends to rapidly diminish. Not that we can't still care deeply about friends with whom we no longer share common interests, but it's probably uncommon for such friends to interact on a regular basis.
History. Nothing ties people together, even people with little in common, than having gone through the same difficult experience. As the sole glue to keep friendships whole in the long run, however, it often dries, cracks, and ultimately fails.
Common values. Though not necessarily enough to create a friendship, if values are too divergent, it's difficult for a friendship to thrive.
Equality. If one friend needs the support of the other on a consistent basis such that the person depended upon receives no benefit other than the opportunity to support and encourage, while the relationship may be significant and valuable, it can't be said to define a true friendship.