One fear consistently expressed about a transition in Egypt is that it would lead to a takeover by the Muslim Brotherhood and the institution of an Iranian-style Islamic Republic. This apocalyptic scenario was implicitly or explicitly evoked by Mubarak and his defenders, with the old man painted as the only thing stopping the mad mullahs from going on a maniacal rampage. A takeover by the Muslim Brothers and an Islamic Republic is not particularly likely in Egypt, however. One thing seen elsewhere is that while Islamist parties have considerable appeal in Muslim and Arab countries, they never seem to really command majority support from voters. So long as Egypt adopts some kind of electoral system with a significant measure of proportional representation then a parliamentary majority for the Muslim Brothers is unlikely. Of course, if Egypt ends up with a non-proportional electoral system, particularly one that gives significant rewards to the largest party, then the country could find itself with an accidental parliamentary majority of the Muslim Brothers.
However, it seems that the Brotherhood is already taking steps to ensure that it does not end up having to rule Egypt. Its leaders have said that they will not be fielding a candidate in presidential elections, an indication that they seem happy enough to remain in opposition. In parliamentary elections they may well follow the example of their fellow in Jordan, where the Islamists fielded sufficiently few candidates that it would have been impossible for them to win a majority. It seems, oddly, that Islamists like being in opposition. This may be because they have spent so long there that they do not have any kind of realistic government programme (the Muslim Brothers in Egypt have a tendency to say "Islam is the answer" when asked any awkward question).
The other reason why the Muslim Brotherhood may choose to lose is the example of what happened elsewhere when Arab Islamists won elections. In 1992 in Algeria an Islamist party looked like winning that country's first ever free elections. The military responded with a coup that plunged the country into a horrific civil war, receiving the full backing of western powers in this attack on democracy. In 2006, when Islamists unexpectedly won elections to the parliament of the Palestinian Authority and formed a government there, the international community responded by cutting off its financial support of the PA and, in the USA's case, attempting to subvert it. It is easy for Islamist parties to conclude, therefore, that political power is a prize that internal and external actors will prevent them from exercising, so it is better just to be a big opposition party rather than the party of government.
One other factor making an Islamic Republic on the Iranian model unlikely is the differing nature of Islam in Egypt and Iran. Iranian Muslims are mostly Shia, while in Egypt Sunnis predominate. Sunni Islam does not feature the kind of hierarchical clergy found in Shia Iran, so there is no monolithic clerical caste to assume the kind of leadership role the ayatollahs in Iran did. It is also noticeable that the Muslim Brotherhood is a mostly lay organisation, with relatively little involvement by Muslim clergy. That is not to say that it could not theoretically impose its vision on society, but it would not be putting Iranian-style Ayatollahs in the driving seat.
In any case, it seems like the Muslim Brothers look more to Turkey, hoping to be like that country's government of friendly Islamists who are no more threatening than European Christian Democrats or the various God Botherers who infest American politics. You may not like these people, but your not liking them does not make their participation in politics illegitimate.
From Hunting Monsters