Crowds of Palestinians came out to see Arafat off as he boarded a helicopter that took him first to Amman, where he then boarded a plane for Paris.
Arafat will receive emergency medical treatment for a potentially fatal blood disorder. Doctors say he has a low platelet count. Platelets are blood components that aid in clotting. A low count can be caused by a number of medical problems, including blood cancers such as leukemia or a liver disorder.
Arafat's mother-in-law, Reemonda al-Tawil, says Palestinians are filled with concern for their leader. "We all hope that he will come back safe to us. It's very moving. Everybody is crying." She said Arafat "is more than a spiritual leader -- he is a father. He is everything to us."
Palestinian Prime Minister Ahmed Qureia said he hopes Arafat will soon return. "We hope, first of all, that he will come back in good health to continue leading the Palestinian people to build [their] independent state," Qureia said.
Qureia said Arafat wants the Palestinians to remain strong.
"His message [is]: Keep united, [and] go ahead, determined to achieve your national right," Qureia said.
Once in Amman, Arafat was laid on a stretcher inside the jet that flew him to a military airport outside Paris. Shortly before his plane left, Arafat told his aides: "God willing, I will come back."
Arafat has named no successor, nor has he appointed an acting president to fill in for him during his treatment.
Should Arafat die, parliamentary speaker Rawhi Fattouh would replace him as Palestinian Authority president for a 60-day period, during which elections would be held.
The health problems of the Palestinian leader are prompting speculation about what might happen to the Palestinian Authority and the independence movement if Arafat dies or is incapable of continuing his leadership.
Nadim Shehadi is an associate fellow of the Middle East Program at the Royal Institute of International Affairs in London. His says speculation about possible political unrest or bloodshed in the Palestinian territories is unsubstantiated.
"It will be not chaos like people are predicting when Arafat leaves. But on the other hand, I am saying that in the long run, there is no obvious replacement for Arafat as a leader who has credibility both inside the PA [Palestinian Authority] and outside," Shehadi said.
Arafat's death would complicate the peace process, as well as Israeli Prime Minister Ariel Sharon's unilateral plan for withdrawal from Gaza and parts of the West Bank in 2005. Shehadi says: "There is no other politician who has the authority to sign any peace agreement with Israel except Arafat."
Shehadi says Arafat is not only the leader of Palestinians in both the West Bank and Gaza, but also of those who live outside the country in refugee camps.
"No Palestinian leader except Arafat can claim to have such authority," says Shehadi.
Shehadi says that although Sharon and Arafat are old enemies, it will be more difficult for the Israelis to deal with the Palestinians after Arafat is gone.
"I think Sharon is probably the person who will miss Arafat most at a time like this because, if Arafat's departure causes problems with the Palestinian Authority or the collapse of the Palestine Authority, then this will make the occupation of the West Bank and Gaza much harder for Sharon," Shehadi says.
Right now, Shehadi says, it is easy for Israel to blame the Palestinian Authority and Arafat for everything. And he notes that the Palestinian territories are heavily subsidized by Western European states.
"But if the Palestinian Authority, after losing its leader, collapses," Shehadi says, "Israel will have to take the whole financial burden of the occupation, with no clear partner to make deals with and no clear peace perspectives."