Re: Pinky and the Brain:
My theory (when the show was still on the air and someone asked) was that they'd time-travel back in time to a specific era (1960s Vegas, the Middle Ages, 1939 New York, etc.) as part of some world-domination scheme of Brain's, but the means of time-travel they used rendered the mice amnesiac about their true temporal origins. The mice would thus assume they actually lived in that time-era, and lived out something similar to their usual lives while in the past... eventually of course, the amnesia wore off, and the mice would head back to the present.
I came up with the "explanation" to suggest why Brain doesn't think television would catch on in "Mice Don't Dance" (at the '39 World's Fair)...
More re: the Flintstones:
Someone asked about Ben Franklin, so....
In an original series episode, the Flintstones and Rubbles visit the Bedrock World's Fair (this episode made during the real-world 1964 New York World's Fair, which got a lot of hype at the time). One of the exhibits is an inventor's time machine, which sends people through time, but only at random (a la a slot machine). Fred and the gang volunteer as guinea pigs, and the families are sent to the "future"----to: ancient Rome (where they're thrown to the lions); October, 1492 (Columbus' voyage to the New World, where Columbus thinks they're stowaways); Camelot (where Fred's forced to joust against the Black Knight for a maiden's hand); Philadelphia in 1752 (where they meet Ben Franklin, think the name "Philadelphia" is a funny name for a city, and help him discover electricity, which they'd never heard of); and finally, 1964's World's Fair, where they get chased by the police. They're soon afterwards yanked back to the Stone Age by the inventor's time machine, tell him the future stinks, and head for home.
(This also is the earliest evidence that blows a hole in the "they're really in a post-apocalyptic future" theory, if the gang considers the bulk of human history as "the future"...).
Think this was the first time they showed the Flintstones traveling through time (other instances I recall: a visit to 25th century Bedrock via the Great Gazoo; the "Jetsons Meet the Flintstones"; a Capt. Caveman cartoon where he, Betty and Wilma IIRC visit what I assume was 20th century Bedrock, in pursuit of a villain named "Futuro" who'd traveled back in time to the Stone Age to use his "futuristic" powers to rob Bedrock blind.).