Solid-state nanopores have emerged as possible candidates for next-generation DNA sequencing devices. In such a device, the DNA sequence would be determined by measuring how the forces on the DNA molecules, and also the ion currents through the nanopore, change as the molecules pass through the nanopore. Unlike their biological counterparts, solid-state nanopores have the advantage that they can withstand a wide range of analyte solutions and environments. Here we report solid-state nanopore channels that are selective towards single-stranded DNA (ssDNA). Nanopores functionalized with a 'probe' of hair-pin loop DNA can, under an applied electrical field, selectively transport short lengths of 'target' ssDNA that are complementary to the probe. Even a single base mismatch between the probe and the target results in longer translocation pulses and a significantly reduced number of translocation events. Our single-molecule measurements allow us to measure separately the molecular flux and the pulse duration, providing a tool to gain fundamental insight into the channel-molecule interactions. The results can be explained in the conceptual framework of diffusive molecular transport with particle-channel interactions.