The only thing that comes to mind right now is Van Heflin's character in Johnny Eager (http://www.imdb.com/title/tt0033774/). Though Robert Taylor's wooden acting actually worked in that movie.

Maybe Kikuchiyo in Seven Samurai. Definitely Lady Kaede in Ran.

The trouble is, when I try to think of any such character, it's easy to see how they would become less interesting if more attention was given to them.