Hazem Salah Abu Ismail, a fiery, and to many frightening, salafy leader (he called Osama bin Laden a "martyr" after the Al Qaeda leader was killed in Pakistan) was tossed from the race because his deceased mother was a US citizen (it's Egypt's own birther controversy; Abu Ismail denies the claim).
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.