Asian Museums

China:

Beijing: Tiananmen Square contains the mausoleum of Mao Zedong. Inside is the preserved body of Chairman Mao. Visitors can line up and walk past the body of the former head of state.

Ürümchi: The Provincial Museum (Xinjiang Province) has an excellent collection of well-preserved, Caucasian 2000-4000 year old mummies.  (Thank you, Dave Roland). See the reviews of two great books about these mummies: The Mummies of Ürümchi or The Tarim Mummies.

African Museums

Egypt:

Cairo: The Egyptian Museum is the granddaddy of mummy museums. It should be the first on anyone's list of mummy museums to visit.

Luxor: The Museum of Mummification is relatively new and well worth a visit. The museum's holdings include a large crocodile, a 21st Dynasty high priest, a cat, a ram, and an ape. The mummy of the high priest is beautifully wrapped. 

South Africa:

Grahamstown: The Albany Museum has an Egyptian mummy from the 18th Dynasty.

Durban: The Durban Natural Science Museum has an Egyptian mummy named Peten-Amun (a priest) from about 300 B.C. 

Pretoria: The National Cultural History Museum has an Egyptian mummy from the Roman period. X-rays indicate that the mummy may be female, but the mummy portrait attached to the coffin is male. Further study is underway.