And then there is the forgotten trio from the late 1950's- early '60's named The Fleetwoods who did soft singing and harmonizing so well that they had 9 Top Forty hits including 2 No.1 hits in the same year. Sample their "Mr. Blue" and "Come Softly to Me".
If you're looking for a totally off-the chain hit from the the 1960's, you should try "Dominique" by The Singing Nun. It's sung completely in French, yet became the #1 song at the end of 1963, not long before the Beatles put a stranglehold on the top of the charts.