Answer:
   
   There isn't one. Many traditional Rabbis tend to wear fedoras, but
   then, so do most of the congregation as part of formal Sabbath wear.
   Some with more Chassidic leanings would wear a Hamburg, a felt hat
   with a flatter brim, no pinches in the hat itself like you would find
   on a fedora. Chassidim themselves tend to wear fur hats. Those
   communities from Russia and eastern Poland wear a "spodik", a brown
   (nearly black) fur hat that is taller than it is high. Those from
   Hungary, Galicia and therabouts wear a "shtreiml", an almost disklike
   hat whose center is felt surrounded by a brown mink ruff. But these
   are worn by the entire community for the Sabbath, and aren't specific
   to Rabbis.
   
   At one point in time, during the 19th and early 20th century, cantors
   -- the ones trained in the melodies and meanings of prayer -- tended
   to wear high Cantorial Caps. They were actually elaborate versions of
   the style of Yarmulka worn amongst Latvian Jews. (The plainer version
   looked something like an old seargent's hat or cooks cap, but in
   black.)