A lot of people would say it was the Chuck Jones era, but I've always been partial to the early '60s cartoons with the weird sound effects. I just found out they were directed by Gene Deitch, who also directed a bunch of Krazy Kat episodes (which I'm not yet familiar with).
Anyway, to tie everything together, here's a pretty good episode about a whale called Dicky Moe. Notice how the captain's peg leg sounds like a sonar blip. Krazy.
Other episodes from the Gene Deitch era put the duo in space, in a swinging bachelor pad, going fishing for muskie, going tiger hunting from the back of an elephant, or in the carribean, all with a vibe-heavy score and weird percussion instead of the work of foley artists for sound effects. It makes sense that Deitch was also the art director for a jazz magazine.