The three fundamental structures carbon-based molecules can form are:

1. Linear: Atoms are connected in a straight line, like in the molecule methane (CH₄).

2. Branched: Atoms are connected in a non-linear fashion, with branches extending from the main chain, like in the molecule isobutane (C₄H₁₀).

3. Cyclic: Atoms are connected in a closed loop, forming a ring structure. This can be simple, like in cyclohexane (C₆H₁₂), or complex with multiple rings fused together.

These three basic structures are the foundation for the immense diversity of organic molecules, forming the basis of all living things.