December 26, 1893 - September 9, 1976: Age 82
"Long Live Chairman Mao for ten thousand years!" — a traditional Chinese praise for the reigning Emperor, this was frequently heard toward the end of Mao's long life. Mao Tse Tung died in 1976 at the age of 82. The cause of death was amyotrophic lateral sclerosis (ALS or Lou Gehrig's Disease; Stephen Hawking has it too) as well as breathing problems caused by smoking. His death came at the end of a long decline (perhaps 5 years) during which various factions vied to win the power struggle that his death would catalyze.
Mao publicly declared in 1956 that he wished to be cremated, but when he died the politburo issued an emergency order to temporarily preserve his body for two weeks. Soon after, it was decided the body should be preserved indefinitely, like Lenin's, in a crystal casket and on view to the public. Unfortunately the Chinese at the time didn't have the technology either to preserve the body or to construct a crystal casket. The Russians did, but China wasn't on good terms the USSR at the time. The embalming problem was relatively easily solved, as the Russians had shared their technology with Vietnam for the preservation of Ho Chi Minh's body, and the government of Vietnam was happy to share it with China.
As to the coffin, they did have a Russian-made coffin created for Sun Yat-sen in 1925 but never used (Sun was entombed in a more traditional manner in Nanjing), but it was too small for Mao's 1.8-meter height. Chinese Embassy employees in Moscow were sent to covertly photograph Lenin's remains and fax the picture back to Beijing. Several different factories were secretly charged with designing and building a suitable casket of crystal.
Two-meter pieces of crystal aren't just lying around waiting to be made into a coffin; the Chinese had to invent a special method of fusing separate plates together. Because the melting point of crystal is more than 2,000 degrees Celsius, the special protective gear worn by the technician fusing the plates together began to smoke in the high temperature, so colleagues had to pour water on him to cool him down while he worked.
Today the body is on view to the public for 4 hours a day; the rest of the time it is stored in a cool basement to promote preservation. Visitors stand in line for long periods, even hours, to view the body. Many report that it looks "waxy", and the guards ensure no more than 15 seconds of viewing, leading to speculation that a) it's a fake or b) it's decaying despite the attempt at preserving it.
Sources: Wikipedia, The Significance of Remembering Mao Zedong, moreorless : heroes & killers of the 20th century