Rabbi Chanina would don his talis gadol on erev Shabbos (Mas. Shabbos 25b, Rambam Hilchos Shabbos 30:2). While this has been practiced by individuals, is it today the practice of any particular segments of Jewry to wear their taleisim for Friday night prayers (and, perhaps, meals)?
The custom of the Teimanin (Yemenites) is to wear a tallis for Friday night prayers. (And I was told by my Teimani neighbor that also when they visit a friend on Shabbos they wear a tallis). But despite this being an old, established custom, many Teimanim who came to Eretz Yisrael have abandoned it, apparently so as not to be different from other Jewish groups.