Palaiologos, the last dynasty of the Empire. Start out as Doux of Epirus. The Doux's son Georgios was a confidant and friend of Alexios I.
Diogenes, for Romanos IV Diogenes. Start out as Doux of Anatolia.
Kantakouzenos, one of the most powerful houses in late Empire. Don't know where they start, but it was on the European side IIRC.
Dalassenos, another prominent family. Start out as Doux of Trebizond.
Laskaris, Emperors during the Nicaean exile. Don't remember where they start in 1066.
Angelos, another house to briefly hold the throne. Start out somewhere on the European side IIRC.
Botaneiates, yet another prominent family that once held the crown.