Mostly video games, books, movies, my random thoughts, and rarely other paper-and-pencil roleplaying games (though I have looked through older D&D editions while designing FrankenFourth, mostly to nail down how complex I want it to be). Some examples:
H.P. Lovecraft is responsible for a lot. I've run numerous FrankenFourth playtest adventures that involved cults of various ancient ones, I ran a whole 4th Edition Dungeons & Dragons campaign around Allabar, I thought up a campaign setting that is orbited by the scorched husks of not-yet-dead ancient ones, and so on.
While playing through Super Mario World and/or Super Mario Wii I got the idea to run a campaign that had the characters go into a crater inhabited by kappa, fungus zombies, and—if they'd kept going—carnivorous plants, giant fish and beetles, etc, all in search of a princess that had gotten kidnapped.
I very recently read Stormbringer, which got me thinking about including alignments as an optional thing in FrankenFourth. Not as personality guidelines, but more your character is allied with a god/god-like entity of chaos or law, which you can beseech for aid, or might impose tasks upon you (similar to the Dungeon World warlock).
Crafting from The Witcher 3: Wild Hunt mostly served as a basis for crafting in both FrankenFourth and Dungeons & Delvers (also alchemical potions). You spend x money to make something, but instead of needing better formula/designs, if you're experienced enough you can spend more money to make better versions (though training requires you to spend enough time and money with a craftsman that's better than you, which becomes progressively harder the better you get).
Oddly the Blood and Wine expansion (also Witcher 3) got me thinking about item sets, as opposed to, say, Diablo 3.
A movie or TV series maybe (I forget what it was) got me thinking about writing/running an adventure that involved an alien invasion. Also been wanting to write/run something to do with a haunted house/location. A bunch of movies are responsible for that one.
I don't remember why I thought up the whole Epiro thing. Closest thing might be the God of War series, but looking back nothing in the campaign really felt inspired by it.
A Sundered World: Player Fragments, the first supplement for A Sundered World, if finally out!
The Paladin is technically the sixth "core" class we've provided an alternative for. If you interested in an alternate class that isn't merely a half-assed reskin, check it out!
By fan demand, we've mashed all of our 10+ Treasure volumes into one big magic item book, making it cheaper and more convenient to buy in print (which you can now do).