The situation in Egypt is interesting, with an unusual number of factions with complex interrelationthips.
As background, Mubarek has been head of a stable, if somewhat repressive, government in Egypt for three decades. There has been a succession issue brewing in Egypt for some time, as Mubarek is 82 and said not to be in good health. He would like to be succeeded by his son, Gamal, who is in his late 40s. However, unlike Mubarek - or his two predecessors, Sadat and Nasser - Gamal does not have a military background, and the power of Egypt's government largely rests on the military. Mubarek favored Omar Suleiman, 74, as his immediate successor, who could then turn the reins over to Gamal after a few years, while the military prefers a younger military person. In 2002 Mubarek moved Ahmed Shafiq, now 69, from the Air Force to a civilian post in a possible step towards making him a compromise candidate.
The current crisis started with street demonstrations early in the week, perhaps by people inspired by what happened in Tunisia. They don't appear to have been highly organized, being more of a "flash crowd" effect from spur of the moment internet coordination, around issues like insufficient food. Around the middle of the week, the Muslim Brotherhood, the banned but largest opposition party in Egypt, started plans to join the demonstrations on Friday after prayers.
Some time thursday, the Egyptian government largely shut down the internet in Egypt, making spontaneous coordination difficult. Meanwhile, the military moved into position in Cairo and other major cities, and declared a curfew. The Muslim Brotherhood swelled the ranks of the protesters on friday, but violence seems to have been limited - perhaps in part because the military is held in higher regard by the population than are the security forces.
While this was going on, Mubarek dissolved the government, appointed Suleiman vice president - the post had been vacant - and invited Shafiq to form a government as prime minister. Basically he's taking this opportunity to cement succession plans in a way that he hopes will be acceptable to the military. What's not clear is to what extent these moves, as well as the military's involvement in the cities, is coordinated between Mubarek and the military.
If they are coordinated, it's most likely that the protests will eventually dissipate, with force if necessary. There would be no power vacuum for a spontaneous movement to fill, and the Muslim Brotherhood has not in the past demonstrated a high degree of coordination - a previous rebellion in Syria was put down fairly easily. The only branch of the Muslim Brotherhood that has successfully gained some power is Hamas, and only over an isolated Gaza voluntarily abandoned by Israel.
In the less likely situation that there's tension between the military and Mubarek, though, it's possible that the Muslim Brotherhood could exploit that tension for a successful revolution in Egypt. That would make for a very interesting situation, since the Muslim Brotherhood is a transnational party with branches in many Sunni Arab states. For example, if the Brotherhood were then able to leverage a revolution in Egypt into power across the rest of Arabia, they would end up being a Sunni organization with power comparable to Shiite Iran - something that does not currently exist.
More likely, though, Mubarek and the military are coordinating - or Mubarek simply remains in charge - and they will be successful in retaining power.