Near the West Bank city of Ramallah, around 200 people protested by the Ofer military prison, with clashes breaking out as demonstrators threw stones at troops who fired tear gas.
Several people were injured lightly and treated at the scene, medical sources told AFP.
In the southern West Bank city of Hebron, around 200 protesters took part in a rally, including foreign activists. An AFP photographer said clashes also broke out there, with Israeli troops arresting at least two people.
In Jerusalem, police said that about 100 Palestinians and Israeli supporters, tried to march through the walled Old City to the flashpoint Al-Aqsa mosque compound but were stopped outside the Damascus Gate.
"There was an illegal gathering of about 100 people," police spokesman Micky Rosenfeld told AFP.
"Police requested everyone to disperse and there was one arrest made... a Palestinian."
In Gaza City, between 200 and 300 people marched from the Square of the Unknown Soldier to the United Nations' Gaza headquarters in a rally organised by the ruling Hamas movement.
Protesters held up maps depicting pre-1948 Palestine, including what is now Israel, and waved green Hamas flags.
The small and largely peaceful marches were in stark contrast to last year's anniversary, when protesters attempted to storm across the armistice line from Syria into the occupied Golan Heights.
Troops opened fire on the demonstrators, with Syria saying 23 people were killed and 350 wounded by Israeli soldiers. Israel said it counted 10 dead, but that none of the demonstrators were killed by Israeli fire.
Three weeks earlier, thousands of protesters in Lebanon, Syria and Gaza had tried to force their way across the borders in a mass show of mourning over the 1948 creation of the Jewish state, known to Palestinians as the "Nakba" or "catastrophe."
At that time, hundreds forced their way onto the Israeli-occupied Golan, where troops opened fire killing four, while a similar yet unsuccessful attempt along the Lebanon border left seven dead, according to UN figures.