And probably out of nostalgia, I really like the Swingle Singers.
My favorite works of theirs are probably their versions of Bach pieces. Those are part of my life's soundtrack, especially when I feel good.
Yet, a cappella music isn't just about the 1960s. It's actually a very broad category in music which spans many genres, from barbershop quartets and boy bands to doo-wop and religious choirs.