The Abu Simbel temple complex was relocated to save it from flooding caused by the Aswan High Dam. The temples stood on the banks of the Nile in Nubia, where the dam's reservoir, Lake Nasser, would have submerged them.
Ramesses II ordered the two temples carved into sandstone cliffs during Egypt's 19th Dynasty, in the 13th century BCE. The larger temple honors Ramesses himself and features four colossal seated statues of the pharaoh. The smaller temple is dedicated to the goddess Hathor and Queen Nefertari, Ramesses's wife.
An international UNESCO-led campaign moved the complex to higher ground between 1964 and 1968. Engineers cut the temples into large blocks, reassembled them inside an artificial rock-and-concrete dome, and preserved their original orientation as closely as possible. The project cost about $41.7 million and involved contributions from 48 countries.
Abu Simbel was not the only Nubian monument moved. Philae, Kalabsha, and other temples were also rescued, so Philae is a related answer to the broader preservation effort but not the complex named in this question.