Although I don't particularly like their music, I think the Beach Boys' vocal arrangements are very well done!
Although it may not have much to do with vocal harmonies, three voices and so on, I think Isley Brothers needs to be mentioned. I prefer their 70's work, mainly from before '77. "Who's that lady" might have some three-voice harmonies actually.
Hey Opethfan1980, have you heard Jefferson Airplane's version of "Wooden ships"? I think it's better than the original actually! It's on their "Volunteers" album.