The only use case I can conceive of is a table of words perhaps for a word game. You access the table just to verify that a string is a word: select word from words where word = ?. But there are far better data structures for holding a list of words than a relational database.
Otherwise, data in a database is usually placed in a database to take advantage of the relationships between various attributes of the data. If your data has no attributes beyond its value how will these relationship be developed?
So, while not illegal, in general you probably should not have a table with just one column.