Recently, research on stem cells has been receiving an increasing amount of attention, both for its advantages and disadvantages. Genetic and epigenetic instabilities among stem cells have been a recurring obstacle to progress in regenerative medicine using stem cells. Various reports have stated that these instabilities can transform stem cells when transferred in vivo and thus have the potential to develop tumors. Previous research has shown that various extrinsic and intrinsic factors can contribute to the stability of stem cells. The extrinsic factors include growth supplements, growth factors, oxygen tension, passage technique, and cryopreservation. Controlling these factors based on previous reports may assist researchers in developing strategies for the production and clinical application of "safe" stem cells. On the other hand, the intrinsic factors can be unpredictable and uncontrollable; therefore, to ensure the successful use of stem cells in regenerative medicine, it is imperative to develop and implement appropriate strategies and technique for culturing stem cells and to confirm the genetic and epigenetic safety of these stem cells before employing them in clinical trials.