A Greater Israel, or Eretz Israel, has been the goal of many Jews almost since the inception of Zionism. It is a Jewish state with biblical borders that includes not just the West bank, Golan Heights, and the Gaza Strip, but southern Lebanon and Jordan as well.

Israel has always portrayed itself as the victim of its Arab neighbors and more recently as the victim of Palestinian terrorists, but the historical record is clear - Israel has never seriously considered living in peace with either its neighbors or the Palestinians. Even before the first World War, Moshe Sharett - who would become the first Israeli Foreign Minister - wrote:

We have forgotten that we have not come to an empty land to inherit it, but we have come to conquer a country from people inhabiting it, that governs it by the virtue of its language and savage culture ... Recently there has been appearing in our newspapers the clarification about "the mutual misunderstanding" between us and the Arabs, about "common interests" and about "the possibility of unity and peace between two fraternal peoples." ... But we must not allow ourselves to be deluded by such illusive hopes ... for if we cease to look upon our land, the Land of Israel, as ours alone and we allow a partner into our estate - all content and meaning will be lost to our enterprise. -- Moshe Sharett, 1914
Zionists were unable to win approval for a Jewish state following World War I - in part because of American assessments of the regional unrest that would follow. Undeterred, Jewish organizations embarked on a campaign of terror against the British mandate controlling the region. At the diplomatic table they appeared willing to accept a two-state solution, but privately their goals were quite different:
[I am] satisfied with part of the country, but on the basis of the assumption that after we build up a strong force following the establishment of the state--we will abolish the partition of the country and we will expand to the whole Land of Israel. -- David Ben-Gurion, Israel's first and longest-serving Prime Minister, 1938
Following World War II and the European guilt over the holocaust, the United Nations voted to create the Jewish state of Israel and a Palestinian state as well. But just one day after the 1947 U.N. vote, Menachem Begin, the commander of the Irgun and Israel's future Prime Minster between 1977-1983, proclaimed:
The Partition of Palestine is illegal. It will never be recognized ... Jerusalem was and will for ever be our capital. Eretz Israel will be restored to the people of Israel. All of it. And for Ever. -- Menachem Begin
Israel was never going to be content with simply expanding her borders; the Arab population also had to be reduced. During the course of the 1948 war, Yigal Allon submitted a detailed plan to David Ben-Gurion for the military conquest of the West Bank, arguing that the Jordan River would provide the best strategic border. He believed that a substantial part of the Palestinian population would flee east because of the military operations:
Our offensive has to leave the way open for the army and the refugees to retreat. We shall easily find the reason or, to be more accurate, the pretexts, to justify our offensive, as we did up to now. -- Yigal Allon
Allon's predictions came true as hundreds of thousands of Arabs fled fearing for their lives. Israel promptly closed its borders to them and has since refused to let them return. In the half-century since, many have of course died, never seeing their homeland again.

Perhaps even more reprehensible is the denial by many Israelis that the Palestinian people ever existed. Israel was founded on the slogan, A people without a land, for a land without a people. Over the years they've come to believe their own propaganda:

There was no such thing as Palestinians, they never existed. -- Golda Meir, Israeli Prime Minister, 1969
The conditions that the Palestinians in the occupied territories live under are chilling. Equally as chilling is the realization that this is not a response to suicide bombings or part of a war on terror, but a decided government plan that has been extant for decades:
We must use terror, assassination, intimidation, land confiscation, and the cutting of all social services to rid the Galilee of its Arab population. -- Israel Koenig, Israel's northern district commissioner of the Ministry of Interior, 1976
Israel has flouted United Nations resolutions since its very conception. The goal has always been one of a Greater Israel. Today Israel offers Jewish settlers in the occupied territories tax-breaks, greatly reduced prices on homes and land, and subsidies for education and health care. There is little reason to believe Israel will abandon the policy of increasing her borders through armed force or of decreasing the Palestinian population through whatever means she finds expedient:
Everybody has to move, run and grab as many hilltops as they can to enlarge the settlements because everything we take now will stay ours... Everything we don't grab will go to them. -- Ariel Sharon, then Israeli Foreign Minister, and current Prime Minister, 1998.
Sources:
monkeyfist.com/ChomskyArchive/interviews/israel3_html
www.palestineremembered.com/Acre/Famous-Zionist-Quotes/
www.cnn.com/SPECIALS/1998/israel/palestinian.view/
http://www.ajds.org.au/Newsletters/January%20newsletter.htm
http://www.prc.org.uk/