Hasn't this been going on for 2,000 years?

Not really. People may have been fighting over the 'holy land' and the territory that makes up the modern state of Israel for thousands of years, but the current conflict is very much a product of the 20th century.
   
Can you give a short history?   
Entire books have been written about the past few centuries in the area, but I'll try.

Historians generally agree that the early Jews were a nomadic people, who began settling in large numbers in Israel starting in 1300 or 1400 BC, and had by 1000 BC conquered, enslaved, or assimilated the previous peoples, becoming an established power. The existence of a unified Jewish Kingdom is uncertain, but by 586 BC the last remaining Jewish political entity, the Kingdom of Judea (centered on modern day Jerusalem) was conquered by the Babylonians, its people deported and taken into slavery.

The remaining Judeans were freed and allowed to return in 539 BC, where they existed as client kingdom for hundreds of years, ruling independently for only 100 years until 63 BC when they were conquered by the Romans.

By 135 AD, a series of unsuccessful Jewish revolts led the Romans to expel all Jews they had not killed or enslaved from the area. The Jewish people would not return as a sizeable population, or an independent political body, for almost 2,000 years.

The Holy Land changed hands a number of times after the Roman Empire fell, though it has been almost exclusively the in the hands of a Muslim governing body since not long after Islam became strongly established in 632, save for a brief two-hundred year span as a series of crusader states that lasted from 1099 to 1291.

By 1516, it was in control of the Ottoman Empire, and there it remained until 1917, when in the aftermath of WW1 it passed to Britain.

Haven't Jews and Muslims always hated each other?

It is no great irony that the two religious groups locked in hatred in our day had far better relations right up until the 20th century. Jews have almost always fared better in Muslim lands then in Christian ones- and when Christian conquered Muslim lands, they often killed or expelled the Jews living there. Jews have been slowly flocking back to the holy land away from Christian oppression, pogroms, and discrimination since the Roman Empire collapsed.
   
How Did Israel Come About?

Ever since their expulsion from the land around 135 AD at the hands of the Roman Empire, Jewish writing and religious text has dealt with the loss of Israel and the desire to return. Many Jews did over the years, but they did not begin to immigrate en masse until 1881, as waves of anti-Jewish violence washed over Eastern Europe.

Years of discrimination and the desire to have a home of their own led to the articulation of the Zionist movement at the turn of the century, whose goals were an establishment of a Jewish state in Palestine. In addition to Jews, this movement gained the support of several groups of people, including, somewhat ironically, anti-Semites who wanted the Jews gone from their lands, Christians, who saw a Jewish state in the Holy Land as part of the fulfillment of Biblical end times prophesy, and state and government leaders who were trying to curry support from their Jewish constituency or ease their guilt over placing immigration quotas which trapped millions of Jews in, or in the path of, Nazi Germany.

The Influx of Jewish Immigrants into Palestine led to considerable, often violent, conflict between the Palestinian Arabs and the Jews. The British, who under the Balfour Declaration of 1917 pledged their support for a Palestinian and Jewish state, and who controlled the Area as a result of World War I, essentially washed their hands of the area after they could do little to satisfy either side and curb the riots and violence. Resolution of the conflict passed to the U.N, who in 1947 issued Resolution 181, which separated Palestine into a separate Jewish and Arab state, with Jerusalem under U.N control.

The Jews accepted the deal, but the Arab groups representing the Palestinians did not, and launched a series of clumsy attacks that were easily repelled. When Israel announced its independence as a Jewish State, it was again attacked by an army of five Muslim nations- but held its own, and when the war was over had established its borders. During the course of the Arab-Israeli war, most of Israel's Arab community, some 700,000 to 800,000 thousand people, fled or were forced into the Palestine region and the neighboring Arab countries. Many of their descendants are still stuck in abject poverty in refugee camps in countries that are still unable to support them.

What makes peace so hard?

A combination of stubbornness, religious fundamentalism, corrupt leadership and the long violent history of Palestinian Terrorism and Israeli retaliation and provocation. The history is much too complicated to summarize here, but every peace attempt has been met with outcries from extremist religious groups, assassination and assassination attempts, and refusals to concede ground on both sides.

To make matters worse, radical individuals on both sides continue to work towards the destruction of either Israel or thwart attempts at a Palestinian State. Suicide, rocket and armed militia attacks by Palestinian or Arab terrorist groups on Israel are commonplace, while radical Israeli militias have slaughtered whole villages, and continue to set up gated, fortified settlements in Arab territory, pushing Palestinian out further and further. It was even Israeli government policy for a while to deport whole towns, raze them, and build Jewish settlements in their place.

Signs of compromise with 'the Zionist entity' are political suicide in the Arab world, and the Palestinian people are usually little more then political tools to create anti-Israel fervor and sweep corrupt regimes into place or help them maintain power, while in Israel continued attacks have given more and more power to fundamentalist governments who view the entire region as their religious right.

Perhaps the most bizarre twist is that, as of 2008 polls, the majority of Israelis and Palestinian support a two state solution, which would simply create an autonomous Palestinian state next to Israel. Attempts to do so have been marred by petty squabbling. Both sides have missed out on chances to put an end to the conflict.

What’s going on now?

The current conflict is centered on the Gaza Strip, which Israel annexed from Egypt during the Six-Day War, and subsequently released to Palestinian control in 2005. Hamas, generally recognized as a terrorist organization, gained democratic control of the Gaza Strip from the more moderate Fatah party in 2007.

Though Hamas has steadily decreased its terrorist activities since its founding in 1987, and become organization mostly dedicated to social welfare and infrastructure creation, it still maintains a militant wing, calls for the destruction of the State of Israel and its inclusion into a Palestinian state, and sponsors rocket attacks on Israeli settlements from Gaza.

In December 2008, a tentative cease-fire between Israel and Hamas ended with both sides declaring the other had broken the truce- Hamas cited Israel’s continued clandestine military operations against Hamas forces, and Israel’s refusal to lift the blockade of the heavily populated Gaza Strip, which denied all but the most basic humanitarian supplies into one of the most poverty stricken areas on earth. Hamas resumed its rocket attacks, firing a few hundred rockets into Israel over the course of a few days. Casualties from rocket attacks are surprisingly rare, but the increasing sophistication and range of the rockets and the sheer volume at which they are launched means that everyone and everything in their range could potentially fall victim at any time.

Israel launched Operation Cast Lead on December 27th, bombing Hamas government and military buildings, as well as police stations, which drew criticism from human rights groups. Just shy of 300 Palestinians were killed, and more then 1,000 wounded.

A few days later ground operations began, and Israeli forces entered the Gaza Strip and gradually encircled and captured Gaza, and remained for two weeks, taking control of areas from which rockets were previously fired, fighting Hamas troops and local militias, and destroying Hamas buildings and weapon sites.

Israel declared a ceasefire on January 17th, and by the 21st had removed all it troops to comply with Hamas demands for ceasefire. Hamas agreed to halt rocket attacks for the week, and Israel has warned it will re-enter Gaza if and when they resume.

What did it accomplish?

The final aftermath of the war, and whether anyone gained anything, is still very much in doubt. Israel claims to have met nearly all its military objectives, but as a result of their offensive has displaced more then 50,000 Palestinians and destroyed nearly 2 Billion dollars in infrastructure. Power, sewer, and water lines are fractured. The BBC reported some 400,000 residents of Gaza were without water as a result of the invasion.

10 Israeli Soldiers have died, 4 of which from friendly fire, and 3 Israeli civilians, with some 518 soldiers and civilians wounded. The Palestinian number is still being tallied. Hamas claims 1,330 dead and 5,300 wounded, the bulk of both totals being civilians, while the Israeli Defense Force has so far tallied its kills at 700 combatants and 150 civilians. Israel has come under international criticism for its loose definition of combatant- that includes police officers, and allows for firing upon civilian buildings such as schools, hospitals and mosques, if said buildings are suspected of Hamas ties.

This includes the Jan 3rd bombing of a mosque which killed 12 people, 6 of which were children, and the Jan 15th shelling of the Gaza U.N. headquarters, which killed 3 people and destroyed tons of food and humanitarian supplies.

Hamas has, for its part, flagrantly flaunted global standards of warfare, allegedly using civilian meat shields, and civilian buildings for cover from which to launch ambushes and rocket assaults on Israeli troops, in an attempt to encourage civilian casualties. In addition, Hamas is suspected of using the chaos to kill, torture, and intimidate members of the more moderate Fatah party.

It's too early to tell whether the invasion will erode public support for Hamas as the populace blames Hamas for what they've brought down on them, as Israel hopes, or whether it will fuel a whole new level of anti-Israel sentiment, as previous reprisals by Israel have done. Regardless, the invasion has created a wave of support for the Palestinian people, with demonstrations against Israel's actions being undertaken in nearly every city in the world, including Jerusalem.

Whether this will bring about any lasting change or just be one more chapter in a far too violent history remains to be seen.