Recurring Plot Devices

Hanna-Barbera has had several recurring plot devices in their animated series.
A male character's wife or girlfriend mistakenly believes her husband or boyfriend is cheating on her. This was used most often in The Flintstones. It has also been used in The Jetsons, The Roman Holidays, and Wait Till Your Father Gets Home.
A male animal falls in love with a female of his species and vice versa. This has been used in The Flintstones, including the movie The Man Called Flintstone, The Jetsons, Yogi Bear, Snagglepuss, Magilla Gorilla, Punkin Puss and Mush Mouse, Ricochet Rabbit and Droop-A-Long, Breezly and Sneezly, Atom Ant, Shazzan, Scooby-Doo, Where Are You!, The Roman Holidays, Jabberjaw, The Scooby-Doo Show, and The 13 Ghosts of Scooby-Doo. 
Animals who travel with humans to foreign countries are never quarantined, and the hotels and other places they stay at are invariably pet friendly. This was used in Jonny Quest, Young Samson and Goliath, Birdman, Josie and the Pussycats, The Harlem Globetrotters, The Amazing Chan and the Chan Clan, Butch Cassidy and the Sundance Kids, Goober and the Ghost Chasers, Valley of the Dinosaurs, The Scooby-Doo Show, The New Scooby-Doo and Scrappy-Doo Show, The New Scooby-Doo Mysteries, and The 13 Ghosts of Scooby-Doo. A notable exception is Jabberjaw, where the title character is subjected to shark ejectors.
When one half of a group is captured by a villain, the other half tries to rescue them, only to be captured themselves. This plot device was used in The Ruff and Reddy Show, Jonny Quest, Shazzan, Josie and the Pussycats, Josie and the Pussycats in Outer Space, and Godzilla.