We explore the high-resolution (lambda/Deltalambda = 25,000; Deltav = 12 km s(-1)) M-band (4.7 - 5.1 mum) spectra of several disk-dominated Herbig Ae (HAe) systems: AB Aur, MWC 758, MWC 480, HD 163296, and VV Ser. All five objects show (CO)-C-12 v = 1-0 emission lines up to J = 42, but there is little or no evidence of moderate- J, v = 2-1 transitions despite their similar excitation energies. AB Aur shows (CO)-C-13 emission as well. The line/continuum ratios and intensity profiles are well correlated with inclination, and they trace collisionally driven emission from the inner disk (R-th less than or similar to 0.5-1 AU) as well as resonance fluorescence to much larger radii (R-hnu less than or similar to 50 - 100 AU for J less than or similar to 10). The temperature, density, and radiation field profiles required to fit the CO emission are in good agreement with models of HAe disks derived from their spectral energy distributions. High-resolution and high dynamic range infrared spectroscopy of CO, and future observations of less abundant species, thus provide direct access to the physicochemical properties and surface structure of disks in regions where planet formation likely occurs.