We present a Chandra X-ray Observatory investigation of the millisecond pulsars in the globular cluster M28 (NGC 6626). In what is one of the deepest X-ray observations of a globular cluster, we firmly detect seven and possibly detect two of the 12 known M28 pulsars. With the exception of PSRs B1821-24 and J1824-2452H, the detected pulsars have relatively soft spectra, with X-ray luminosities 1030-1031 erg s–1 (0.3-8 keV), similar to most "recycled" pulsars in 47 Tucanae and the field of the Galaxy, implying thermal emission from the pulsar magnetic polar caps. We present the most detailed X-ray spectrum to date of the energetic PSR B1821-24. It is well described by a purely non-thermal spectrum with spectral photon index Γ = 1.23 and luminosity 1.4 × 1033Θ(D/5.5 kpc)2 erg s–1 (0.3-8 keV), where Θ is the fraction of the sky covered by the X-ray emission beam(s). We find no evidence for the previously reported line emission feature around 3.3 keV, most likely as a consequence of improvements in instrument calibration. The X-ray spectrum and pulse profile of PSR B1821-24 suggest that the bulk of unpulsed emission from this pulsar is not of thermal origin, and is likely due to low-level non-thermal magnetospheric radiation, an unresolved pulsar wind nebula, and/or small-angle scattering of the pulsed X-rays by interstellar dust grains. The peculiar binary PSR J1824-2452H shows a relatively hard X-ray spectrum and possible variability at the binary period, indicative of an intrabinary shock formed by interaction between the relativistic pulsar wind and matter from its non-degenerate companion star.