I use single-column tables all the time -- depending, of course, on whether the app design already uses a database. Once I've endured the design overhead of establishing a database connection, I put all mutable data into tables where possible.
I can think of two uses of single-column tables OTMH:
1) Data item exists. Often used in dropdown lists. Also used for simple legitimacy tests.
Eg. two-letter U.S. state abbreviations; Zip codes that we ship to; words legal in Scrabble; etc.
2) Sparse binary attribute, ie., in a large table, a binary attribute that will be true for only a very few records. Instead of adding a new boolean column, I might create a separate table containing the keys of the records for which the attribute is true.
Eg. employees that have a terminal disease; banks with a 360-day year (most use 365); etc.
-Al.