I've seen some Jewish homes with photos of respected rabbis framed on the wall. When historically did this Jewish custom begin? How widespread is it today?
The custom is based off the pasuk in Yeshayahu 30:20, which says, וְהָי֥וּ עֵינֶ֖יךָ רֹא֥וֹת אֶת־מוֹרֶֽיךָ "your eyes will watch your teacher." The Gemera in Eruvin 13b explains that looking at ones teacher/Rebbe increases ones understanding and sharpens ones mind. Indeed this would show that the custom before putting pictures of tzadikim on the wall was to look at them while they are still living, so this may be the start of the idea of putting tzadikim on the wall which occurred later on (not sure when). As to how widespread it is, most orthodox homes that one goes to have them.
From my own personal observation, I have noticed that photos of gedolim (even if not relatives) have been adorning the walls of many homes for the last few decades. I wouldn't be surprised if the trend has increased in more recent times by the availability of inexpensive photography and that many מוסדות צדקה have included such pictures within large envelopes encouraging donations to their institutions.
The following is an opening attempt to answer your question focusing on the history/period of origin of the custom. This provides a benchmark that can be extended to an earlier date when people submit more samples.
The following two American personalities were born in Trondheim, Norway: the late David_Abrahamsen and his younger brother Prof. Samuel Abrahamsen (a past head of Jewish Studies at Brooklyn College).
I remember an old Abrahamsen family photo from Trondheim in 1927 hanging on the wall of the latter's apartment. In that picture, a photo of Rav Yitzchak Elchanan Spektor zt"l was hanging in a place of honor in the Abrahamsen home in pre-WW2 Trondheim. The same family picture was published in a book in Norwegian by a member of that family. The picture of Rav Spektor appears on the upper right corner and is partially cut off:
A good place to search for earlier such photos hanging in the background of family pictures might be the hundreds of yizkor books that were published.