I grew up watching Saiyuki or Monkey! as it was known in it's British dubbed version as well as Le Manège enchanté or The Magic Roundabout in it's English language version and in both of those cases the dubs were made by actors fully in on the joke and much better for it.

Some of the early Jackie Chan films were much funnier in the dubbed versions too and often the actors seemed to know what they were up to (especially in Project A where English dialogue was dubbed into English and still out of sync).