Inspiration can come from many places. It's great when it just hits and results in something new and unique. However, that kind of moment tends to be rare. Instead, I often find myself needing to take inspiration from something already existing and trying to turn that into something that feels fresh and new. That is easier said than done. I'll share some of what I find sometimes helps me. Hopefully at least one of you out there finds it useful or at least interesting. In this case I'm talking about home games that you don't plan to have published. Some things, like improperly lifting things, can get you into hot water if you try to publish it. The distinction between these different types can sometimes be muddy but that's fine. They are meant as a starting point and to help inspire you.
Distilling is one of the easier methods and also a common favourite. What you do is start with something you like or at the very least find interesting for one reason or another. Then, you start to hack away and remove details or elements to get it into a form that contains what you see as the essence of what you started with. Since this is naturally based on the interpretation of the person who is doing the process, it can be very personal and even create different results if you try it after some time has passed. Many complex works also have more than one thread or idea that runs through them. This brings even more variation to the technique. Once you get this essence, you can then build back up to something new. When you are done, it should look different than what you started with.
Let's try an example. Star Wars has a long history and also quite a few well liked characters. Let's try to hack off some of the characters first. We'll remove Lea and Han Solo, leaving us with Luke and Darth Vader. We can decide that the central idea between those two was something along the lines of temptation, with Luke tempting Vader to the light (successfully, at the end) and Vader trying to tempt Luke to the dark side. Now we can start trying to build it up. Maybe we can have a character who leads armies, as the second in command, against a rival faction. He wants his son to take his side and succeed him but his son feels conflicted about what he would have to do since he is disillusioned with his own faction. At this point, we can have the son change sides and throw our characters into things. Or, we can decide that it might happen and let your players influence things to see where it might go (decide based on their actions or have some modifier bonus based on their actions to a roll). If we keep filling out the specifics, we can end up somewhere different than where we started pretty quickly. What if it was from his first taste of combat? What if it was because of a particularly sneaky move that was done (poisoning water, assassinating a child king, etc.)? Was this event a normal occurrence or a common exception? Maybe they don't want to switch sides but want no part of things until someone with a very good diplomacy bonus comes along? The key is not to keep too much of the original and not to think of where we started from when building back up. We want something distinctly different when we build the scenario back up.
Sometimes, we can just shamelessly borrow ideas or scenarios from something. When talking about something reasonably complex, you can often borrow one or two things pretty easily without it being too obvious or too blatant. It still needs to be small enough that it can be fit into the scenario seamlessly. If you steal the entire story of Star Wars, someone will notice. If you steal just the Han Solo arc of coming back at the end to help unexpectedly for something other than money, you might get away with it. Maybe just once though.
Coat of Paint
There are a lot of things out there to read, watch, and play. Enough that you can't go through all of it in one lifetime. This means that if you know of something obscure enough, you can take significant chunks of it, cover it with some fresh paint, and use it. Old space opera stuff tends to work quite well, though you'll need to be a bit careful to avoid comparisons to Star Wars when that wasn't your intention. Obscure historical events also work quite well for this sort of thing. No matter where you are, there tends to be at least one place in the world or one period of time where your players have no idea what happened. The Russian Time of Troubles is one of my favourite situations since it makes for very interesting and easy conversions. It's really a great source of inspiration for a particular kind of campaign and story.
It has to be obscure though. If you use this kind of technique, you are taking a large part from the original. You can of course distill a historical event, but that would be distilling and not adding a coat of paint, really.
Instead of removing things to get down to the essence, you can add things. One thing I've seen used successfully, though not as commonly as the above, is to take two or more different ideas, story lines, or even collections of tropes and throw them all in. Though the elements on their own aren't very unique, the way they fight each other can end up being so. It typically works well for more comedic games from what I've seen. It can work for more serious games as well, as so many works have multiple plot lines and elements, but it is generally harder to pull off.
Your Own Campaigns
Everything I've mentioned above can be attempt on your own campaign games or even published adventures. However, I'd be careful with doing this on a group that has seen the original. You run the risk that it will be too similar to the original. You can probably get away with distilling, but the others may come off too blatant and similar. It can also defeat the original purpose of coming up with new ideas for your tabletop game.