We have performed a set of prototypical quantum calculations of the electronic structure of a none-atom helium plasma over wide ranges of temperature and density. These calculations reveal the presence of very tightly bound quasimolecular states in high-density plasmas, even at temperatures high enough to ionize fully the component atoms. The results of the study suggest that there are four regimes in a plasma, dependent upon the relationship of the electron wavelength to the interionic spacing: low-density atomic, intermediate-density screened atomic, high-density quasimolecular, and very-high-density homogeneous.