Marathon Des Sables
The original multi-stage desert foot race. Every year 800 competitors (mainly from the UK and France) tackle 150 miles of desert running in 6 stages over 7 days carrying all their provisions (except water) for the week. Takes place in the Sahara in Morocco. 
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This tends to be on everyone's "to do" list and the cut-off times are generous enough for the whole thing to be walked. It's popularity has led to a huge number of similar races appearing all over the world. It's popularity means that to do this race you should expect to wait 3 years, and pay 4 grand.
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Race Reports
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My attempt (2009)
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Similar Races
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Racing the Planet - 4 Multi day races in the Atacama, Gobi, Sahara deserts and Antarctica