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Carbon by itself doesn't form all that many compounds, but there are a lot of molecules with carbon plus a few other elements (like oxygen or hydrogen or nitrogen).

The reason is that while carbon can (and in fact often does) combine with oxygen, nitrogen, hydrogen and a lot of other elements, it's not all that much more energetically favorable for it to do so as opposed to bonding with another carbon atom. Since each carbon atom can have up to four bonds, this gives carbon a lot of flexibility in making complicated molecules.

Silicon also can form up to four bonds, but it bonds with oxygen much more strongly than it bonds with other silicon atoms, so if you have silicon and oxygen around, you wind up with pretty much exclusively silicon dioxide until you run out of either silicon atoms or oxygen atoms.

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