In the first year of comics (i.e. 1939-40), Batman even carried a handgun. But the character evolved quickly into the "shall not kill" hero we know today.
During the heyday of the TV series, the comics reflected the silliness. Only in the 70s, with abysmal sales, did DC put Denny O'Neal in charge of the Bat. His scripts were much darker and brought Batman closer to his roots as the Dark Knight Detective. Denny invented, among other villains, Ra's Al Ghul, Clayface II, Hugo Strange and Man-Bat. That was the time when Robin left the batcave and Bruce lived in a penthouse at Wayne Enterprises (as opposed to the Manor).
The realistic art by Neal Adams also cemented Batman's turn towards grittiness that eventually culminated in The Dark Knight Returns.