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It happens to me sometimes. However, my ideas are usually so strange that it has not been done before (I'm a surrealist writer). I had to scrap a few stories before either because they were already done before or because I didn't like the idea anymore. A lot of time travel stories have been written, so it is likely that, when you're working on a story with that in mind, it's probably been done before. That was one of the ideas I had to toss.
I did get mad over this one title that I wanted to use for a short story only to find out that James f***ing Patterson already used that title. I hate that guy. stare I probably wouldn't mind so much if it wasn't so difficult for me to think of titles.

Either drop this notion of originality or give up writing. You'll never have an idea that bears no resemblance to something else.

Even the Discworld example you gave is based off Native American beliefs.

I'd also say sometimes an idea needs to be "ripped off" a few times before someone does it right.

I think less about shortcomings and more about where my guesses diverge from the actual plot. Because sometimes it's not really a flaw in the story or writing that catches my attention, but sometimes I think something is more significant than it is, and my mind starts trying to follow that detail, and I end up daydreaming something quite different than the actual story. Often I'll go back and revisit that moment in time and if the impression is still strong I'll use it to spring board a story of my own.

Ehhhh, not really. I mean, it's impossible to create a completely new idea, right? And what really matters is the execution--that's what makes your idea stands out and, hopefully, worth reading.

Any plot can be broken down to the point where you could be talking about any number of books movies, television shows, video games, and so on. Male protagonist with dark hair and green eyes finds out he has special powers and goes on adventures with his best friend and a very intelligent girl. What do you think I'm talking about? Because two book series are sitting on my shelf that are both correct answers.

The point is whether or not its been done before comes down to the details. Just because your premise is similar doesn't your book will be. The Two series that fit that description I gave have similarities but I would never suggest that they are similar.

I wouldn't worry too much about "its been done before" and worry more about "How can I make this idea my own?" "How do I take this and make it different and new"

The last book I worked on was about Vampires. Which lets face it are super over done and have been done and done again since the 18th century. But rather than give up on an idea I had almost four years ago and had been sitting in the back of my mind maturing, I decided to do so much research on vampire mythology, and how vampires have affect real world culture that I would be able to make my vampires interesting, different, not ridiculous and still consistent with some form of mythology.( actually they are consistent with all forms but that's a complicated explanation for another time)

Never throw out ideas even if you won't use them now because you don't think you can make it your own or don't think you could make it work at all, in ten years maybe you'll see or hear something and think "If I do that with this it will be something amazing and mine". And that's worth it.