Okaaay. Different approach today. Going to try to ignore the abhorrent grammar, and use of vocabulary, and just try to answer as best I can.
Because, to have a favorite inspiration...that would be...you know...impossible.
If there were one thing that always inspired you no matter what you were working on, one go-to source for "the process of being mentally stimulated to do, or feel something, especially to do something creative" (Definition by way of a Google search), one could just go to it any time they needed any idea, for anything. Right? Yeah. So...ugh.
Also, grammatically, this is kind of asking, "Remember that one time you were really inspired to do something? Tell us about that one time." Your favorite inspiration would be the one time you were inspired that you enjoyed the most.
I don't think that's what we're going for here.
Is this what you meant maybe? OK then. Why didn't you say so?
Inspiration for my games, and game ideas comes from a wide variety of things, and sources. It depends very much on the subject of the game, the style, and atmosphere I'm going for, the mood I'm in, and whether I am trying to do something new, or recapture an old vibe from back in the day.
For example, when trying to get inspiration for Traveller, I look at what kind of PCs I have first. If I am getting an exploration motif out of the team (like we're aiming for with our upcoming Traveller: Beyond game), I will check out Sci-Fi artwork, books, films, comics, and games focused on discovery, and exploration. If on the other hand it's a mix of combatants, bureaucrats, scientists, spies, and such (Like our current Operation: PALADIN campaign), I am going to look into things that are more conspiracy, espionage related.
I guess if I had to pick a favorite source of inspiration for my games, I would say artwork tends to be a major inspiration. I will get more ideas from a cool illustration than a written work more often than not.
On a related note, Anime, and Manga of various sorts are often great catalysts for ideas. Again, the nature of the Anime/Manga series will inspire a related genre, or idea. I get a lot of comedy ideas by watching comedies. I am inspired to run a military mecha game after seeing a great military mecha Anime.
For Superhero gaming, comic books, especially older ones, and ones with more obscure titles, and characters are key inspirations. I love the forgotten heroes, and villains of the forties, through to the sixties. A gonzo villain updated a bit, with a new name, and a redesigned costume always makes a big impression on my players, mostly because I'm jazzed about them.
Music, songs to be more precise, used to inspire me a great deal, but less so over the last 5-10 years. It's getting harder, and harder to find modern stuff that gives me the ideas that pieces from the 60s and 70s did.
My last great source for inspiration is conversation with friends, especially fellow gamers. One discussion will lead to a joke, which will set off an idea, and presto, I have a concept for a scenario I can insert into my game world.
So that's about the size of it. Art, Anime/Manga, Comic Books, Classic Rock, and Good Conversation are my favorite inspirational sources.
How about you?
Oh, and about fixing the question, really, there's no need to thank me.
Just doing my job.