We calculate that significant quantum interference effects can be observed in elastic electron transport through acyclic molecules. Interference features are evident in the transmission characteristics calculated for cross-conjugated molecules; significantly, these effects dominate the experimentally observable conduction range. The unusual transport characteristics of these molecules are highlighted through comparison with linearly conjugated and nonconjugated systems. The cross-conjugated molecules presented here show a large dynamic range in conductance. These findings represent a new motif for electron transfer through molecules that exhibit both very high and very low tunneling conductance states accessible at low bias without nuclear motion. In designing single molecule electronic components, a large dynamic range allows a high on/off ratio, a parameter of fundamental importance for switches, transistors, and sensors.