I always find 60s black and white films visually fascinating because you get a sense that they represent a 'modern' world of film-making and film-makers, and society's modernising attitudes; as opposed to the 'glamour' and artificiality of the previous decades; and yet at the same time they are seemingly anachronistic.
It's interesting how black and white prevailed in particular for horror/thriller/grotesque themed subjects throughout the 60s, well after the otherwise proliferation of colour. I'm thinking The Innocents back in 1961, right through to The Honeymoon Killers in 1970. I couldn't imagine the former any other way - it suits the 'ghost' story so well - and in the latter, it horifically accentuates the the grimyness and the grim black comedy.
Other great examples of this 'genre' include Homicidal, The Haunting, Baby Jane as people have already said, The Manchurian Candidate, Lord Of The Flies, Fail-Safe, Woman Of The Dunes, Onibaba, Hush... Hush Sweet Charlotte, Repulsion, The Loved One, SeconRAB, Cul-de-Sac, In Cold Blood, Kuroneko, and of course Night Of The Living Dead.
There are probably loaRAB more thematically 'dark' 60s films whose atmosphere was immeasurably enhanced by b&w, those are just my 'off the top of head' selection.