I'm not very familiar with all the characters, but for the ones I know...
Batman - Gregory Peck
Robin - an adolescent Dean Stockwell
Batgirl - Sally Field, circa
The Flying Nun
Alfred - Dick Powell
Commissioner Gordon - Burt Lancaster
The Joker - Henry Fonda, in villanous spaghetti-western mode
The Penguin - W.C. Fields, seconded
Catwoman - Josephine Baker
The Riddler - Sterling Hayden
Mr. Freeze - Marlon Brando
The Scarecrow - Ray Bolger is hard to beat, but how about Jimmy Stewart?
Poison Ivy - Joan Crawford and Bette Davis can fight over the role
Harley Quinn - Natalie Wood
Ra's Al Ghul - Jose Ferrer