The high-energy X-ray and ultraviolet (UV) radiation fields of exoplanet host stars play a crucial role in controlling the atmospheric conditions and the potential habitability of exoplanets. Major surveys of the X-ray/UV emissions from late-type (K and M spectral types) exoplanet hosts have been conducted by the Measurements of the Ultraviolet Spectral Characteristics of Low-mass Exoplanetary systems (MUSCLES) and Mega-MUSCLES Hubble Space Telescope Treasury programs. These samples primarily consist of relatively old, “inactive,” low-mass stars. In this paper we present results from X-ray observations of the coronal emission from these stars obtained using the Chandra X-ray Observatory, the XMM-Newton Observatory, and the Neil Gehrels Swift Observatory. The stars effectively sample the coronal activity of low-mass stars over a wide range of masses and ages. The vast majority (21 of 23) of the stars are detected and their X-ray luminosities measured. Short-term flaring variability is detected for most of the fully convective (M ≤ 0.35 M ⊙) stars but not for the more massive M dwarfs during these observations. Despite this difference, the mean X-ray luminosities for these two sets of M dwarfs are similar, with more massive (0.35 M ⊙ ≤ M ≤ 0.6 M ⊙) M dwarfs at ∼5 × 1026 erg s−1 compared to ∼2 × 1026 erg s−1 for fully convective stars older than 1 Gyr. Younger, fully convective M dwarfs have X-ray luminosities between 3 and 6 × 1027 erg s−1. The coronal X-ray spectra have been characterized and provide important information that is vital for the modeling of the stellar EUV spectra.