Israeli forces have fired on groups of protesters at borders with the Palestinian territories, Syria and Lebanon.
Reports say that at least 12 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 around the time of its creation.
Responding in a televised address to Sunday's violence, Israeli Prime Minister Benjamin Netanyahu said he hoped "calm and quiet will quickly return, but let nobody be mistaken, we are determined to defend our borders and sovereignty".
Later on Sunday, security forces in the Egyptian capital Cairo fired warning shots and tear gas to break up protests outside the Israeli embassy.
UN Secretary General Ban Ki-moon has called for calm and urged all sides to show "utmost responsibility".
In a statement, he said there was an "unsustainable status quo in the Arab-Israeli conflict, which is only thrown into sharper relief by the profound political changes now under way in the region" and called for a renewed effort to reach comprehensive peace in the region.
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.
Clashes at the Qalandiya checkpoint in Ramallah continued for hours, with dozens of Palestinians injured.
Palestinian protesters threw stones at Israeli security forces, who fired 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 two 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 the closing stages of the 1967 Six-Day War.
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 10 people have been killed and scores wounded.
"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.
"Israel will have to bear full responsibility for its actions," the foreign ministry said.
However, one Israeli official told AFP: "Syria is a police state. Demonstrators do not randomly approach the border without the prior approval of the central government."
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.
Police in Jordan fired tear gas to break up protesters gathering at a village near the Israeli border.
In Cairo, police used tear gas and warning shots to drive back a crowd of several hundred people who were attempting to reach the Israeli embassy in protest.
The Mena state news agency said at least 24 people were injured in the clashes.
Meanwhile in Tel Aviv, Israeli police are investigating whether an Arab-Israeli lorry driver deliberately ploughed into pedestrians, killing one Israeli man.