This page is pretty much a perfect representation of what I loved about Batman and Robin as a kid — the mysterious disappearance, the frightening reappearance, the banter, the goofily-masked villains.
(From Detective Comics #553, August 1985. Written by Doug Moench. Art by Klaus Janson.)
I believe the animated show, BTAS, took this approach as well: we had goofy villains to an extent, dramatic entrances and exits, and fun banter. The show was able to provide a child-friendly homage to the Bronze Age.
I like Denny O’Neil’s approach to the Dark Knight best, though, and how he was able to weave in human depths into Bruce’s character without having him angst all the time.