We investigate the origin of asymmetry in various measured current-voltage (I-V) characteristics of molecules with no inherent spatial asymmetry, with particular focus on a recent break junction measurement. We argue that such asymmetry arises due to unequal coupling with the contacts and a consequent difference in charging effects, which can only be captured in a self-consistent model for molecular conduction. The direction of the asymmetry depends on the sign of the majority carriers in the molecule. For conduction through highest occupied molecular orbitals (i.e., HOMO or p-type conduction), the current is smaller for positive voltage on the stronger contact, while for conduction through lowest unoccupied molecular orbitals (i.e., LUMO or n-type conduction), the sense of the asymmetry is reversed. Within an extended Hückel description of the molecular chemistry and the contact microstructure (with two adjustable parameters, the position of the Fermi energy and the sulphur-gold bond length), an appropriate description of Poisson’s equation, and a self-consistently coupled nonequilibrium Green’s function description of transport, we achieve good agreement between theoretical and experimental I-V characteristics, both in shape as well as overall magnitude.