There is an infinite stream of podcasts paying attention to the Arab-Israeli conflict and plenty of good ons at that. (see my label Israel) Lecture series such as those that are compiled in the UChannel Podcast give you nearly every week a couple to choose from.
What is exceptionally good at these is that the experts are invited to speak and one is receiving a much better frame of reference than by merely reading the newspapers. One such expert is David Makovsky from the Washington Institute for Near East Policy who lectured about Middle East Challenges to the Obama Administration. I can recommend this lecture for getting some insight in the political intricacies between Israel and the Palestinians.
I was surprised, for example, once again, to be presented with a representation of affairs in which Fatah and Egypt have been wanting Israel to be hard on Hamas in Gaza. Makovsky makes this case just as Asher Susser and Jacob Dayan on UCLA's Israel Studies podcast. I have made very skeptical remarks about this when I reviewed Dayan's lecture, but surely the political point is true: both Fatah and Mubarak's regime in Egypt are threatened by Hamas and are each incapable of doing much and therefore it is welcome to them if Israel does the dirty work.
More UChannel Podcast:
Good climate for everyone (global warming),
Robots and War,
Sudan and the fallacy of nationhood,
Lakhdar Brahimi on Afghanistan and Iraq.