The elections on Thursday are expected to be a test of strength between the Fatah movement and resistance groups such as Hamas.
"This is democracy and freedom, and God willing we will choose the right people who will serve our needs," Rahma Hamid, a school principal who voted in a village near Ram Allah, said.
In the West Bank, roughly 1000 candidates were competing for about 300 seats on 26 local councils, mostly in villages, during the first phase of the elections. A similar poll in the occupied Gaza Strip was delayed because of registration delays.
Long lines formed in front of polling stations for what was also the first Palestinian ballot in the occupied territories since Arafat was elected president in 1996.
On 9 January, Palestinians will choose a successor to Arafat, whose death has triggered a wave of diplomatic initiatives.
Strong favourite to win that election is Fatah candidate Mahmud Abbas, who has opposed armed struggle and is expected to try and revive negotiations.
But Fatah, which wants a state on land captured by Israel in 1967, faces a tougher challenge in the municipal ballot from Islamist groups standing in Palestinian elections for the first time - though still boycotting the presidential vote.
Poll and results
A good showing for supporters of Hamas resistance group in the municipal elections could make it tougher for Abbas, though a Jerusalem Media and Communication Centre poll showed Fatah with a nearly 42% rating compared to 26% in June.
Hamas has slipped to 20% from 22%, according to the poll.
Voting began at 07.00 local time (0500 GMT) and ends at 19.00, with results expected shortly after.