BECAUSE the process of galaxy formation is most unlikely to be perfectly efficient, there is a strong possibility that some baryonic gas remains outside collapsed structures such as galaxies and clusters of galaxies. What fraction of the baryonic content of the Universe resides in this intergalactic medium (IGM) and what physical state it is in are open questions. Here we use observational limits on the density of neutral hydrogen in the IGM, on the lack of deviations from a black-body spectrum of the cosmic microwave background (MBR), and on the extragalactic component of the soft X-ray background (XRB) to constrain the state of the IGM. From the lack of MBR fluctuations, any energetic IGM (containing as much energy as the binding energy in galaxies) is inferred to be smoothly distributed on scales greater than galactic. This rules out hot IGM models for the origin of the hard X-ray background, as well as the hypothesis that cosmic explosions may have given rise to cosmological structure on scales larger than galaxies.