As biosensing devices shrink smaller and smaller, they approach a scale in which single molecule electronic sensing becomes possible. Here, we review the operation of single-enzyme transistors made using single-walled carbon nanotubes. These novel hybrid devices transduce the motions and catalytic activity of a single protein into an electronic signal for real-time monitoring of the protein's activity. Analysis of these electronic signals reveals new insights into enzyme function and proves the electronic technique to be complementary to other single-molecule methods based on fluorescence. As one example of the nanocircuit technique, we have studied the Klenow Fragment (KF) of DNA polymerase I as it catalytically processes single-stranded DNA templates. The fidelity of DNA polymerases makes them a key component in many DNA sequencing techniques, and here we demonstrate that KF nanocircuits readily resolve DNA polymerization with single-base sensitivity. Consequently, template lengths can be directly counted from electronic recordings of KF's base-by-base activity. After measuring as few as 20 copies, the template length can be determined with <1 base pair resolution, and different template lengths can be identified and enumerated in solutions containing template mixtures.