Omar Suleiman, Mubarak's long-time intelligence chief and confidante, was kicked from the race because the Presidential Elections Commission ruled that his petition to run didn't receive signatures from a wide-enough range of locations (Egyptian rules require 30,000 signatures, with at least 1,000 of those from each of 15 different governorates). And Khairat al-Shater, the top Muslim Brotherhood political strategist, was disqualified because a 2006 security conviction by the Mubarak government hasn't been voided.
Others were disqualified because of political convictions during the Mubarak era, or disputes over the leadership of their political parties, and in the case of Ashraf Zaki Barouma, over allegations of draft-dodging in his youth.
With the election looming, it's unclear what comes next. Some may be reinstated, others not. Shater, Abu Ismail and Suleiman all lodged appeals of the ruling today. The electoral commission has promised a final candidate list on April 26, less than a month before the vote. Street power as a solution can't be ruled out. The Muslim Brotherhood called tens of thousands of its supporters to Tahrir Square last week, and a lawyer for Abu Ismail promised a "major crisis" if his man isn't allowed to run.
The Muslim Brotherhood's Freedom and Justice Party appears best placed, since it nominated another candidate, Muhammed Mursi in case Shater was disqualified. But a recent poll by Egypt's Al Ahram Center for Political and Strategic Studies indicates it may not do them much good. The disqualifications leave Ahmed Shafiq and Amr Moussa, two long-time servants of Mubarak, as front runners. The poll, conducted before the disqualifications, found Islamist voters had high enthusiasm for both Shater and Abu Ismail, but not for Mr. Mursi.