Inspiration can occur any time you watch or read something and say "What if?" What if they'd lost/won? What if that plan/treaty/cure worked or didn't work? Look at some basic concept, conflict, or dilemma that caught your attention, that you found evocative, and just noodle on alternate outcomes.
Personally its like with anything I watch or read. If I'm watching say, Battle Star Galactica, and I say this would have been the best story ever if only they hadn't done x, y or z. Or if on the other hand they had only done this! (x,y or z) then this would have been the best, most coolest or simply a better story. Then you sit back and say how can I write this story as it should have been without plagarizing this other author's work.
Change the names, change the races, change the characters, change the space or fantasy empires but keep that stomach gripping emotional struggle or epic battles 'how they should have been' or 'I am your father twist (in a world without jedi)' or whatever.
Make it yours, make it unique, yet go for that thing that always irked you about star trek/B5/Star Gate/GSG etc and make it cool instead of sucky. et - I don't want static characters or I don't like how they always seem to be about to have epic battles but always gimik their way out of them, lets have some thunder and destruction people! or if only they didn't fight all the time and just made peace and wild naked monkey love in the streets of their nudist colony with all those super interesting blue skinned, telepathic and oh so-so sensitive aliens, instead of trying to gun them down with blaster pistols in the streets all the time or 'whatever' your pet peeve was. It will become cool. All you have to do is stay true to yourself and try to save that.....? and you will inevitably be forced to write something new and unique and most of all cool! Because I guarantee that if you love it, you're readers are going to love it a lot more than if you are uninspired.
The Deposed King