I'm really not sure how to answer this, but let's have a go.
It feels like a question to ask a GM, and I very rarely run games (not a whole lot of confidence, love playing, have a lot of friends who really enjoy GM'ing). That's not to say there aren't plenty of things I come across that spark off the desire to create in a role play sense - either to enhance my playing or in a setting creation sense for a game I'll never run. Then again, I could think about the things that have inspired other people to run my favourite games.
Let's start with the latter.
I'm going to go back to the Final Fantasy Noir homebrew game. I've never played a Final Fantasy game to completion. I got a fair way through FF7 on a friend's PS1 before the memory card got wiped and her family got rid of FF7 because they'd nearly finished and couldn't face working through it again and I've watched other people play chunks of 8, 9, 10 and I think 12, but I've never played one all the way through.
But they are beautiful, detailed games, crafted with love.
I love this bit of music and think this is a fantastic cover.
So that might be my favourite inspiration for a game I've played in. The guy running 'Final Fantasy Noir' is a huge fan and did his best to recreate the vastness of the worlds, managing to create a very engaging game in the process. I don't think it would have been my inspiration, but I'm grateful to it.
What about things that inspire me as a player? It depends, but I like using games to try out things I'd not dare to do - to test my own morality, I suppose. I played a Ravnos in a Vampire game once. Her name was lost in the mists of time, but she went by Mathilde at the point the game started. She was a bully and a trickster - she revelled in causing emotional pain to other people. I am not that kind of person but I wanted to understand it, wanted to play with the concept. I was inspired by the idea that vampires don't feel emotion and slowly (or otherwise) lose their connection with humanity, and I wondered how one might deal with that. I guess I was inspired as much by the setting as the desire to explore what could have been a part of me if I'd been a different person.
And if I were running games... I'd love to run something set in Genevieve Cogman's The Invisible Library. I think Lords of Gossamer and Shadow would work really well: the similarities between the settings and the freedom offered by the LoG&S system mean I wouldn't have to make many changes. But I've got a couple of ideas for games set in the world(s) of LoG&S I'd want to use it for first, so that will have to wait.
I've talked about the book before. Parallel worlds with a Library connecting them (very L-space!), with the librarians of the Library trying to track down copies of all the books in existence. The universe is divided between Law (represented by the Library and dragons, although the two have their own agendas and don't work together) and Chaos (represented by the fey races). Librarians don't age whilst in the Library, need to be smart and athletic to retrieve the books, and have access to certain magics by calling on the Library. Parallel Earth's mean a setting players can recognise but which can be twisted to the GM's control.
Reckon a lot of fun could be had with that.
But mostly it's characters I'm inspired to create, as evidenced by the Character Concepts tab above. I've got several to add when I have time to write up properly, and it's all sorts of things that can inspire. Sometimes I just want to create my own version of an archetype; often something I read will send sparks flying; sometimes I'll pinch an idea from a friend or someone or Twitter (I try to get consent when I notice I'm doing it!) - and as with 'Mathilde' above and several of the cyberpunk characters, sometimes I want to explore something opposite to me.