Built in 1255 for the Capitano del popolo (municipal officeholder), the Bargello appears to be the older public building in Florence. Its austere crenelated walls and tower served as model for the more famous Palazzo Vecchio at the end of 13th century.
In 1261, the Podesta, the highest magistrate of Florence city council, settles down in the new castle. In 1574, the Podesta is abolished by the Medici and the police chief of Florence, the bargello, replace him in the building. Used as a prison, the Palazzo del Bargello remained the headquarters of the florentine police until 1859, and then opened as a national museum in 1865.
You visit it more for the amazing collection of sculptures it houses than for the palace itself - but the place deserves to appear in this collection of castles :-)
(pictures of the sculpture collection would be irrelevant in this comm but I'll soon post it in my own LJ, if you're interested)