The Far Ultraviolet Spectroscopic Explorer (FUSE) ultraviolet spectra of eight giant and supergiant stars reveal that high-temperature (3×105 K) atmospheres are common in luminous cool stars and extend across the color-magnitude diagram from α Car (F0 II) to the cool giant α Tau (K5 III). Emission present in these spectra includes chromospheric H Lyβ, Fe II, C I, and transition region lines of C III, O VI, Si III, and Si IV. Emission lines of Fe XVIII and Fe XIX signaling temperatures of ~107 K and coronal material are found in the most active stars, β Cet and 31 Com. A short-term flux variation, perhaps a flare, was detected in β Cet during our observation. Stellar surface fluxes of the emission of C III and O VI are correlated and decrease rapidly toward the cooler stars, reminiscent of the decay of magnetically heated atmospheres. Profiles of the C III λ977 lines suggest that mass outflow is underway at T~80,000 K and the winds are warm. Indications of outflow at higher temperatures (3×105 K) are revealed by O VI asymmetries and the line widths themselves. High-temperature species are absent in the M supergiant α Ori. Narrow fluorescent lines of Fe II appear in the spectra of many giants and supergiants, apparently pumped by H Lyα, and formed in extended atmospheres. Instrumental characteristics that affect cool star spectra are discussed.