The habitable zone (HZ) around a star is typically defined as the region where a rocky planet can maintain liquid water on its surface. That definition is appropriate, because this allows for the possibility that carbon-based, photosynthetic life exists on the planet in sufficient abundance to modify the planet's atmosphere in a way that might be remotely detected. Exactly what conditions are needed, however, to maintain liquid water remains a topic for debate. In the past, modelers have restricted themselves to water-rich planets with CO2 and H2O as the only important greenhouse gases. More recently, some researchers have suggested broadening the definition to include arid, "Dune" planets on the inner edge and planets with captured H2 atmospheres on the outer edge, thereby greatly increasing the HZ width. Such planets could exist, but we demonstrate that an inner edge limit of 0.59 AU or less is physically unrealistic. We further argue that conservative HZ definitions should be used for designing future space-based telescopes, but that optimistic definitions may be useful in interpreting the data from such missions. In terms of effective solar flux, S(eff), the recently recalculated HZ boundaries are: recent Venus--1.78; runaway greenhouse--1.04; moist greenhouse--1.01; maximum greenhouse--0.35; and early Mars--0.32. Based on a combination of different HZ definitions, the frequency of potentially Earth-like planets around late K and M stars observed by Kepler is in the range of 0.4-0.5.