The cheetah has never been domesticated. Domestication implies controlled breeding and artificial selection, but tame cheetahs have been a symbol of elegance for thousands of years. The Ancient Egyptians were the first recorded civilization to keep these cats since at least 1550 BC. Wild adults would be captured and trained to hunt alongside carts. Adult cheetahs were preferred over cubs since they had already perfected their hunting skills in the wild and would not need as much training. Kept blindfolded like hawks, the cheetah would only be unleashed once the prey had been flushed out. Half-sport half-spectacle, this practice was reserved for the royal and the affluent. The need to capture wild adults would have kept the sport from ever becoming a practical hobby like falconry, especially due to the already low natural populations.
The Egyptians passed this practice onto the Persians and they, in turn, introduced it to India*. An emperor known as Akbar the Great (1542-1605) was the first Indian royal to keep cheetahs. The story goes that in the year 1555 Akbar received as tribute a hunting cheetah known as Fatehbaz. Akbar went on to own more than one-thousand hunting cheetahs. This practice was passed down through generations of Indian princes well into the twentieth century. In fact, the sport was so well known throughout India that during the British Raj that Asiatic cheetahs were known as hunting-leopards (the Dutch word for cheetah is, in fact, still based off that description: jachtluipaard).
Below is one of the only videos of this practice in action. Today, with the cheetah population declining and greater public pressure against such private menageries, the sport has virtually disappeared.
It is undeniably exciting to watch and I must admit I feel more than a small pang of jealously, imagining what it must have been like to see in person.
*While I mostly discuss its practice in India, the sport and keeping of tame cheetahs also notably appeared in the courts of Charlemagne, Genghis Khan, and Italian nobles during the Renaissance.
Sources: Life with an Indian Prince, pictures-of-cats.org, africahunting.com, Wikipedia,
the glyptodon 
neutrino_cannon
March 30, 2012 at 10:14 am
While it is true that there are higher populations of falcons in the wild, captive breeding of birds of prey was not accomplished until the 1960s (or about ten years until captive breeding of cheetahs was figured out).
This has led to some gender-bending misconceptions. Because female falcons are bigger, many cultures assumed that they were the males.
theglyptodon
April 7, 2012 at 6:54 pm
That’s pretty interesting. I didn’t know they were still wild birds at that point. Thanks for the info.