The present invention provides a cell culture medium formulation that supports the in vitro cultivation, particularly in suspension, of mammalian cells, particularly epithelial cells and fibroblast cells, and methods for cultivating mammalian cells in suspension in vitro using these media. The media comprise a basal medium and a polyanionic or polyanionic compound, preferably a polysulfonated or polysulfated compound, and more preferably dextran sulfate. The present invention also provides chemically defined, protein-free eukaryotic cell culture media comprising an iron chelate and zinc, which is capable of supporting the growth (and particularly the high-density growth of mammalian cells) in suspension culture, increasing the level of expression of recombinant protein in cultured cells, and/or increasing virus production in cultured cells.