The first, of course, was Jonny Quest. The title character, the young son of scientist Dr. Benton Quest, would fly around the world with his father, his father's partner Race Bannon, and his friend Hadji, solving all sorts of problems and foiling evil. And their dog Bandit, too, of course...
Then there was Space Ghost (the original, serious one). It actually consisted of two different cartoons; Space Ghost, with the futuristic super hero and his two proteges, and Dino Boy in the Lost Valley, which was a sort of Lost World homage with cave men, dinosaurs, and a young boy getting into and out of various perils.
Birdman and the Galaxy Trio came next, with superhero Birdman (again, the original, serious, one) fighting various villains in one half of the show, and the Galaxy Trio, an otherwise forgettable threesome of outer space superheroes doing likewise.
The Herculoids was somewhat high-concept for its day; it's set in the future, on an alien planet, but the protagonists are a family from a high-tech society that have decided to settle on a savage planet and live a primitive lifestyle, and defend the planet against technological encroachments. There are a bunch of different intelligent races on the planet, and there are many opportunities for peril, as well as the family's collection of semi-sentient alien-companions. There were a few crossovers with Space Ghost, if I remember correctly.
Shazzan is one of my personal favorites, a riff on Aladdin, with a brother and sister who together can summon the genie Shazzan. The kids seem to be from the modern world, but the series is set in a very fantastic Arabian Knights sort of setting. The plots are interesting, up to the point where they wrap up with the kids putting their rings together and having the genie save the day.
Mightor was one of the segments in the Moby Dick and Mighty Mightor show, which featured a prehistoric superhero (complete with secret identity) foiling various villains seeking to harm the peaceful inhabitants of a prehistoric village.
The Banana Splits Adventure Hour consisted not only of the costumed rock band playing some (actually fairly decent) songs and telling jokes, but with four recurring series as well; the Arabian Knights, which featured a band of good-hearted rogues (actually, a strongman, a magician, an acrobat prince seeking to get his throne back, his cousin who is an expert in disguise, and a shape-shifter) trying to overthrow the evil usurper of Baghdad, Danger Island, which featured a family shipwrecked on an island with pirates, dangerous animals, and savages who liked to paint their bodies like skeletons; and the Three Musketeers, which was pretty much as the name implies. There was also a fourth, Micro Ventures, which was pretty dull, and consisted of the family being shrunk down to very small size and using their dune buggy to escape now-giant ants.
The Adventures of Gulliver featured the titular character seeking a treasure, with an evil pirate trying to get the map from him, always foiled by the tiny people of Lilliput.
Sealab 2020 (once again, the original, not the later parody) was a neat science fictiony type adventure series, centered around an underwater research station. This was about the last of Hanna-Barbera's "serious" adventure shows.
After this point, they stuck with the predictable formula of cheap gags and silly situations (with the exception of the truly amazing Pirates of Dark Water, which deserves a post of its own), but for a time there in the 1960's and 70's, they had a great raft of solid adventure stories that could definitely serve as inspiration for a game today.
And with that, I leave you with this über-cool boardgame-themed Jonny Quest promo from Boomerang...
Also, please don't forget the Adventures Dark and Deep Bestiary Kickstarter has just one more day to go! 900 monsters, suitable for most OSR-type games, all under one cover. Can you help get us to having an illustration for each and every one?