What makes carbon special?
I think that the link that Ron mentioned answered the question adequately, although let me add my own take.  (What makes carbon special and versatile?)

I heard that the reason Carbon is able to make such stable multiple bonds is that its orbitals are close enough to its nucleus that they form extremely effective overlap when bonding.  It is therefore the best atom because it is the smallest atom that can form four bonds.  When you have 5 valence electrons already and can only make 3 bonds with 1 lone pair, that usually leads to weird bent shapes (although Nitrogen is also pretty common in organic compounds).

It's kind of like, which hotel is more versatile in booking large families—a hotel with four open rooms right next to a breakfast bar (Carbon), a hotel with three open rooms and a full room right next to a breakfast bar (Nitrogen), or a hotel with any amount of open rooms, except you need to walk a mile for breakfast (any other element)?