Yale University has agreed to return most of the Inca artifacts it has housed since Professor Hiram Bingham “rediscovered” Machu Pichu and brought back over 4,000 pieces from the site. The collection includes items such as mummies, ceramics, and bones. Bingham “rediscovered” Machu Pichu back in 1911, bringing it to world attention.
Part of this new agreement has been to promote a traveling exhibit with the pieces, which will eventually find a permanent home at a local museum in Cuzco, Peru, scheduled to coincide with the centenary of Bingham’s “finding” of the site. It will also allow a few selected pieces to remain at Yale a while longer for further scientific research.
In the past a many other countries, and native people the world over have struggled to recover items that were taken during periods of colonization and dominance by foreign groups. During the 1990s the USA passed the Native American Graves Protection and Repatriation Act (NAGPRA), requiring museums to inventory their collections and consider returning certain items, although this only applies to federally recognized indigenous groups.
The British Museum has had to deal with a number of cases concerning repatriation, but their response has usually been non-compliance with request from countries such as Egypt and Greece.
You can read more about this issue from an article in the BBC concerning the Yale-Machu Pichu case, or from an article in Suite 101 discussing whether repatriation is a passing fad or not. Wikipedia also has an entire index dedicated to repatriation, divided by cultures.