Half of the Gaza Strip's 1.5 million people would leave if they could, according to one poll.
But obtaining a permit to cross into Israel or Egypt is getting harder every day. In better times tens of thousands of Palestinians entered Israel to work. But today just a few dozen get out.
Since the Islamic militants from Hamas took control of Gaza in 2007 Israel has tightened its blockade of the crowded coastal territory. Israeli officials say Hamas rule of Gaza has created the need for tighter security restrictions. But ordinary Palestinians are caught between the two sides and students seeking education abroad, businessmen meeting their Israeli partners, or people simply wishing to see relatives in the West Bank find it almost impossible to get out.
Even Palestinians needing urgent medical treatment in Israel's hospitals are finding it more difficult to obtain travel permits from the Israeli authorities.
According to Israel's Physicians For Human Rights the number of medical permits being granted has fallen dramatically, and even tougher screening means that almost 40 percent of Palestinians with permits miss their medical appointments.
Amiram Gill, the group's director of advocacy, told ABC News Thursday: "Israeli policy has changed. Everything else has stayed the same inside Gaza, in terms of the number of sick people and the lack of treatment facilities. Israel is making it harder for people to leave."
Some reports say Palestinians are even trying to bribe local doctors in return for fake medical records. Gill said his group was aware of isolated cases but said the odds are stacked against those who try it.
"Once the person gets to the Israeli checkpoint the screening process is so thorough and detailed, someone faking an illness would almost certainly be discovered," he said.
But some Palestinians who do get out don't return. Israel's defense ministry claims that this year of the 7,000 Palestinians who got out, some 500 have never gone back. Most make their way to the Palestinian-controlled areas of the West Bank and "disappear" in search of work.
At Gaza's southern end its border with Egypt has also been sealed. On average in 2009 it has only opened once a month for just a few days allowing around 2,000 people out each time.
At the main border crossing in Rafah the culture of bribing Palestinian and Egyptian officials is well known among local residents. It costs anywhere between $500 and $1,500 for so-called "coordination." The money buys a place on a list of people allowed out when the border eventually opens.
Hazem Riyashi, 27, told the Associated Press he paid a middleman $1,000 in July to help get him into Egypt. But the man vanished with his money. Riyashi says he won't give up and is already saving up for another bribe.
"I think everybody should leave Gaza," he said. "Even the air smells cleaner abroad."