After the recent cease-fire between Israel and Hamas, some pundits are calling for a renewed effort to establish peace between Israel and it's Palestinian/Arab/Muslim enemies. I believe that such peace is impossible. It does not take an expert to see that the barriers to peace are insurmountable without radical changes to the cultures of that region. That is not to say that there is no point in trying to contain the conflict, but I think that we should be realistic about what can be achieved with the traditional strategies, and then we should think about alternative strategies.
Below, I'll spell out the barriers to peace from each side.
1) No reasonable Israeli would be willing to live under a state that is dominated by Palestinians (or Arabs or Muslims). The political cultures of those societies are frighteningly primitive. Add to that the Jewish experience as a minority in Europe and the decades of hostility from Arabs, and Israelis could not expect to have any freedom or security in an Arab-dominated state. They will rightfully fight to preserve Israel's independence and Jewish (or Western) majority.
2) Semi-reasonable (nationalist) Israelis will go to great lengths to preserve their own security, even at the expense of the security of non-Israelis. They will occupy neighboring lands if these lands can be used as staging grounds for attacks. They will limit the mobility of the residents there, close their borders, and occasionally launch military incursions if they feel threatened. Unless terrorist attacks from the occupied territories end for a substantial period of time (a decade or two), the occupation will not end.
3) Fanatical Israelis will attempt to annex the neighboring lands and create a "greater Israel".
4) Outside fanatics (largely in the US) will support Israel under all circumstances, even when it is promoting fanatical policies.
1) No reasonable Palestinian will tolerate living under Israeli occupation, particularly when it severely infringes on security and social/economic activity or pressures them to leave their current homes.
2) Semi-reasonable Palestinians will resent the Zionist invasion of Palestine. If their family was exiled, they will demand the right to return to areas within the 1967 borders, and/or a large compensation. They will not trust Israel.
3) Fanatical Palestinians/Arabs will demand that Israel be incorporated into a Muslim-dominated polity, where Jews will at best be second-class citizens.
4) Outside fanatics will support the Palestinians regardless of what they do.
Even if everyone were reasonable, this would be difficult to resolve. The Israelis and Palestinians would have to find a way that each of them could live in their own community without infringing on the other. Given the intermixing of their settlements (particularly in and around Jerusalem) and the differences in their political cultures, and the duration and intimacy of their conflict, this would be a challenge.
However, most people are not reasonable, in that they are strongly biased towards members of their own group (I call this "semi-reasonable", because they can still empathize with the suffering of outgroup members, but they discount it by a substantial factor). Combine this fact with the existential threat felt by each side, and peace is nearly impossible.
But it's worse than that, because fanatics are influential on each side (these people take no consideration of outsiders), and these fanatics are egged on by outside support and their ranks are swelled by each flare-up in the conflict.
The traditional strategy:
One strategy is to address the outside actors. The Neocons place their focus here: they hope to eliminate the outside support for the Palestinians, thereby weakening the fanatics and their military capacity. They hope that this would create an absolutely one-sided military situation on the ground. I think that such ideas are pure fantasy. It would essentially require that the USA occupy the entire middle east, and Israel establish a totalitarian regime over the Palestinians (which would inevitably have cracks).
Another strategy is to establish cease-fires that will allow trust to develop (allowing the semi-reasonable people on each side to come into alignment). This has worked in other conflicts, but as described above, I don't think it would be nearly sufficient here.
A more radical strategy is to develop compassion between the warring sides by building friendships between Israelis and Palestinians (essentially, making people reasonable). While this is a noble endeavor, I don't think that it can make sufficient inroads to have a strong political impact on its own.
An alternative strategy:
I can hardly say that I have a strategy. Maintaining cease-fires and building cross-group connections will probably be helpful under any circumstance, even if they cannot create lasting peace. The only peaceful outcome that I can envision is a radical change to the Israeli and Palestinian group identity. For instance, this could arise from a threat from an outside enemy that they each view as especially foreign and threatening, but I cannot provide any realistic prediction of what that enemy might be (robots? aliens? zombies?). The best that I can think of is for them to be absorbed into some sort of post-national cosmopolitan society. To the extent that such a society is developing, the Israelis have a decent connection to it. The issue is more how to entice the Arabs to refocus their attention to this society and give up their ancient obsessions. Even after the fundamental political and economic changes occur, it will probably take a generation or two for the old group identity to weaken sufficiently to allow peace to be established between Israel and Palestine.