Why is carbon so special? What makes carbon form so many compounds?

Carbon is special due to two unique properties: 1) Catenation: carbon atoms can bond with OTHER carbon atoms to form long chains, branches, and rings. Very few elements do this (silicon does slightly, sulfur forms short chains). This gives carbon the ability to form an almost unlimited variety of skeletal structures. 2) Tetravalency: carbon has 4 valence electrons and can form 4 covalent bonds. This means carbon can bond with H, O, N, halogens, AND other carbons simultaneously. Combined effect: one carbon can bond to 4 other carbons, which can each bond to 4 more, creating enormous diversity. Compare: nitrogen is trivalent (3 bonds), oxygen is divalent (2 bonds) — far fewer possible structures.