Assuming that the Brotherhood does manage to assume effective control in Egypt, it will mark a substantial change in the Egypt-Israel dynamic. First, Egypt's shift from a largely secular military dictatorship to a democratically elected though primarily theocratic government would mark a change in Israel-Egypt relations similar to the change that occurred in Persian-Israel relations when the Pahlavi monarchy collapsed in Iran and was replaced by the Islamic Revolutionary government. As is often the case with new Islamic governments in the Middle East, the Brotherhood will need to establish its credentials in the region by showing its ability to stand up to Israel and advance the interests of the Palestinian nationalist movement. Unlike when this happened with new governments in Iran, Iraq, Syria or Lebanon, Egypt's extreme proximity and intertwined history make the Brotherhood's actions particularly significant.
For example, the largely lawless Sinai Peninsula has been a major source of sabotage and terrorist activity, with attacks on oil and gas pipelines occurring with great frequency. Moreover, the Sinai is the primary gateway into Israel for both African economic migrants and potential infiltrators. While Israel continues to move to complete a secure border fence along its Egyptian border, it is possible that the Brotherhood will act either directly or indirectly to undermine Israeli interests in that area. In fact, in the days since the presidential election, a rocket attack along the Egyptian border killed an Israeli civilian and the response to the attack killed three militants on the border. Escalating the situation may be an effective way for the Brotherhood to establish control and allow it take certain actions under the guise of acting against Israeli aggression.
Of greater significance will be the Brotherhood's stance on the Hamas-run Gaza Strip. The Mubarak government took an ambivalent and pragmatic view on Palestinian nationalism and took a relatively hard line on Gaza after the Hamas takeover, resisting pressure from the rest of the Arab world to open the Rafah crossing and end the blockade. While restrictions on Rafah have eased somewhat in the wake of the Egyptian Revolution, the Egyptian military has retained significant control of the region in an attempt to prevent the entry of Hamas men into the Sinai and to curb the flow of weapons into Gaza. However, it is unlikely that the Brotherhood would view the regulation of Rafah as a major priority, and would likely see a benefit in allowing a freer flow of goods into Gaza. Moreover, the Brotherhood could win regional credibility and put Israel in an unfavorable position by facilitating the flow of goods into Gaza through Rafah in contravention of Israel's restrictions on goods into Gaza.
Indeed, if the Arab Spring has had any broad based impact, it has been shifting many of the prior military/secular dictatorships into more theocratic and religiously oriented governments, primarily because religiously based organizations such as the Muslim Brotherhood were the primary opposition to repressive secular governments such as those in Egypt, Syria or Tunisia. However, it is not clear at all that the replacement of those secular governments with theocratic ones will lead to improvements in the lives of the very people whose large scale protests swept the old dictators out of power. As in late 1970s Iran, the call of young university students for Ayatollah Khomenei provided extremely ironic as Khomenei's return in 1979 shut down many of the liberal institutions whose protests brought him back to power. If nothing else, bringing an Iranian or Saudi style government to power in Egypt completes the reorientation of the Middle East powers away from pan-Arabist nationalist ideologies that were championed by men like Gamal Abdel Nasser and Saddam Hussein. The major power players in the region: Egypt, Saudi Arabia and Iran, will continue to angle for ideological and military supremacy in the region.
Lastly, because the Muslim Brothers are not limited to Egypt, their taking power in that country can have broad effects on their operations in other nations such as Jordan, Bahrain and Syria. With the financial and operational backing of a sovereign nation, the Muslim Brothers and their affiliates can make significant inroads in taking control in other governments that hang in the balance, most notably in the ongoing civil war in Syria.