Israeli forces have fired on groups of protesters at borders with the Palestinian territories, Syria and Lebanon.
Reports say that at least eight people have died and dozens more have been injured.
In one incident, thousands of Palestinian supporters from Syria entered the Golan Heights, Israel says.
Palestinians are marking the Nakba or Catastrophe, their term for the founding of the Israeli state in 1948.
Hundreds of thousands of Palestinians fled or were forced out of their homes in fighting after its creation.
Clashes have been taking place at four separate borders or crossing points - at Erez in Gaza, near Ramallah in the West Bank, on the Golan Heights and at the border with Lebanon.
The BBC's Jon Donnison, in the West Bank town of Ramallah, said this year's Nakba protests have been given impetus by the uprisings in countries across the Middle East and North Africa.
Our correspondent, at the Qalandiya checkpoint there, says there is a stand-off now, but dozens of Palestinians have been injured.
Palestinian protesters have been throwing stones at Israeli security forces, who have been firing tear gas and rubber bullets.
On the occupied Golan Heights, the Israeli military said it had only fired warning shots as a large number of protesters tried to breach a border fence near the village of Majdal Shams.
But reports said at least four people had been killed and dozens injured.
Israel's army says this is a "serious" incursion. Brig Gen Yoav Mordechai said soldiers were still trying to control the crowds and that dozens of protesters had crossed.
The army has reportedly sealed off Majdal Shams and is carrying out house-to-house searches for infiltrators.
Israel seized the strategic territory from Syria in 1967.
On the Lebanon-Israel border, a large number of protesters also approached the crossing with Israel.
Dozens of buses had brought protesters to the area under the rally slogan of "March for the return to Palestine".
Lebanese soldiers had fired in the air to try to disperse the protesters, who were chanting: "By our soul, our blood, we sacrifice ourselves for you, Palestine."
Gen Mordechai says Israeli troops fired as demonstrators began vandalising the fence.
Lebanese military officials say four people were killed.
"We are seeing here an Iranian provocation, on both the Syrian and the Lebanese frontiers, to try to exploit the Nakba day commemorations," Gen Mordechai said.
A spokesman for the UN peacekeepers in southern Lebanon called on both sides there to show restraint.
Syria denounced Israeli actions in the Golan Heights and Lebanon as "criminal", Agence France-Presse news agency reported.
On the Israel-Gaza frontier, at the Erez border crossing, Israeli troops opened fire with tanks and machine guns, injuring dozens, Palestinian medical officials said.
Meanwhile in Tel Aviv, Israeli police are investigating whether an Arab-Israeli lorry driver deliberately ploughed into pedestrians, killing one Israeli man.