The centre-left Zionist Union promises to repair relations with Palestinians and the international community.
Mr Netanyahu, whose party has trailed in opinion polls, vowed on Monday not to allow the creation of a Palestinian state if he wins a fourth term.
The economy and living standards have emerged as key issues.
Polls opened at 07:00 (05:00 GMT) and are due to close at 22:00.
Results could be declared soon afterwards, but a lengthy period of negotiations over the formation of the next coalition government may follow.
Under a sunny Jerusalem sky, voters have been turning out at a polling station surrounded by election posters, party volunteers on hand for a last-minute push. Among them is the banner of Likud, the right-wing party of Benjamin Netanyahu, with the slogan “It’s us or them… only Likud”.
But Israel’s Prime Minister for the past six years knows it could well be “them” after today’s vote. Behind in the last opinion polls, he faces the political fight of his life. Even if he loses to the opposition Zionist Union, though, he still stands a better chance of building a coalition. The centre of gravity of Israeli politics is largely on the right – the Zionist Union could struggle to find the partners needed for a 61-seat majority.
Mr Netanyahu has campaigned on his core issue of security, shoring up his right wing vote by effectively ruling out a Palestinian state. But for his opponents – and for the majority of voters – the number one issue here is the cost of living that has soared under his watch. And that is where they believe his weakness lies.
No party has ever won an outright majority under Israel’s proportional representation voting system, and neither side is expected to get more than a quarter of the votes in Tuesday’s election.
Opinion polls published before the weekend suggested that the centre-left Zionist Union is likely to win the most seats.
However, the BBC’s Kevin Connolly in Jerusalem says that it might still be possible for Mr Netanyahu to form a coalition government even if his Likud party fails to top the poll.
The main players
Benjamin Netanyahu: Victory for his Likud party could mean a fourth term for the veteran of Israeli politics. His hawkish stance on the Palestinians and Iran have made him popular with the right but a divisive figure.
Yitzhak Herzog: The co-leader of the centre-left Zionist Union electoral alliance, Mr Herzog has accused Likud of depressing Israeli living standards and campaigned against Mr Netanyahu’s foreign policy. He has tried to counter Mr Netanyahu’s accusations he is “soft” by pointing to his special forces background.
Tzipi Livni: Mr Herzog’s co-leader in the Zionist Union, Ms Livni is a prominent advocate of seeking more cooperation with the Palestinian Authority.
Moshe Kahlon: A former Likud welfare and communications minister under Benjamin Netanyahu, Mr Kahlon’s centre-right Kulanu party could play kingmaker in a coalition.
An end or new era for Netanyahu?
Will the outcome revive the peace process?
International issues, from Israel’s relationship with the United States to concerns over Iran’s nuclear programme, have been one focus of the campaign.
But many of the candidates have concentrated on Israel’s socio-economic problems, including the high cost of living and slow economic growth.
Israelis attend a right-wing rally in Tel Aviv’s Rabin Square March 15, 2015.
Right-wing supporters have been rallying but the centre-left is expected to win most seats
Moshe Kahlon at a polling station in Haifa, Israel, 17 March 2015
Moshe Kahlon, leader of the new Kulanu party, could play the role of kingmaker in coalition talks
The future of the city of Jerusalem has also been a central election issue.
Mr Netanyahu has consistently accused his centre-left challengers of being willing to relinquish Israel’s claim to Jerusalem as its indivisible capital in peace talks with the Palestinians.
On Monday, Mr Netanyahu spoke at the Har Homa Jewish settlement in East Jerusalem and said he was the only person who could ensure the city’s security.
He said no Palestinian state would be formed were he to remain prime minister.
Palestinians seek East Jerusalem – occupied by Israel since the 1967 Middle East war – as the capital of a future Palestinian state.
But Zionist Union party co-leader Yitzhak Herzog has accused Mr Netanyahu of “panicking”.
Visiting the Western Wall, one of the holiest sites in Judaism, on Sunday, Mr Herzog pledged to “safeguard Jerusalem and its residents in actions, not just words, more than any other leader”.
- Nearly six million Israelis voting for a new parliament (Knesset)
- Votes are cast for a party, rather than individual candidates
- 120 seats up for grabs, though electoral system means no single party will achieve a majority
- Blocs of parties must command at least 61 seats to form a government
- President has seven days in which to appoint an MP with best chance of forming a government
- Candidate has initial 28 days to put workable coalition together