This invention provides media that support the growth of primate pluripotent stem cells in feeder-free culture, and cell lines useful for producing such media and other purposes. Conventionally, it has been necessary to grow pluripotent embryonic cells on feeder layers of primary embryonic fibroblasts, in order to prevent them from differentiating. It has now been discovered that standard culture media conditioned by special cell lines can be used to support proliferation of pluripotent stem cells while inhibiting differentiation in an environment free of feeder cells. This invention includes mesenchymal and fibroblast-like cell lines obtained from embryonic tissue or differentiated from embryonic stem cells. Methods for deriving such cell lines, processing media, and growing stem cells using the conditioned media are described and illustrated in this disclosure.