Some embodiments of a medical device anchor system include an anchor device that receives a catheter (or other medical instrument) and secures the catheter in place relative to a skin penetration point. In some embodiments, the anchor device can secure the catheter in an operative position relative to the skin without the use of sutures or skin tapes. In particular embodiments, the anchor device can be adjusted to a folded condition so that subcutaneous anchors are partially rotated prior to removal from the skin penetration point.