We investigate equilibrium bidding in standard auctions with asymmetric reserve prices. For example, the auctioneer sets a low reserve price for one subset of bidders and a high reserve price for others. In the first-price auction we identify an equilibrium reserve price externality whereby bidders facing a high reserve price benefit from a reduction of opponents' reserve prices. We also document cases where introducing asymmetric reserve prices can increase the auctioneer's expected revenue compared to an optimal, but uniform, reserve price---even if all bidders are ex ante identical. An extension of the model characterizes equilibrium bidding in asymmetric first-price auctions with asymmetric reserve prices. The use of asymmetric reserve prices in auction design is discussed.