It's really nothing to worry about. Really.
Don't lose sleep over it.
Even if anyone stole your idea, chances are they expressed it differently--because it's next to impossible they wrote it *just* like you would have. Though that may anger you, it shouldn't be a worry to a real writer. Everyone steals ideas to an extent. Take Shakespeare. Half of his plays were based on previously written stories. Shakespeare is the king of idea theft. Does anyone really care? No. I even have a short story I wrote based on the premise of Othello, but am I worried I "stole" Shakespeare's or his predecessors ideas? No. Because it may be the same idea at the heart, but the expression is so completely different, they're still very, very different stories.
And it probably won't happen to you. Chances are you're the one who's the thief, even if you don't know it. Chances are your ideas are similar to ones that are already out there--consciously, subconsciously, or even just coincidentally. But your vision is probably completely different. If anyone ends up stealing your idea, the situation will probably be exactly the same, which really isn't something you should worry about.
If you want a good movie/short story to read on this, watch Secret Window based on the Stephen King short story, or read the actual story. I recommend the movie--even though it's King--simply because it has Johnny Depp. Part of the premise is that an unknown hick writer shows up at Johnny's house one day and accuses him of stealing one of his stories, and slowly begins to destroy Johnny's life until he can either prove he didn't steal it, or gives the other guy credit for it. In the end, we realize all of this is ***SPOILERS*** in his head, and no theft ever happened at all.
But seriously, don't worry. You automatically have a copyright on any original material you've written (or painted or composed, etc.), no matter what. That's just your right as an artist, and chances are you'll never have to worry any more about it.
The only real worry I can think of is certain contests. Always read contest rules completely. Some of them have fine print that says--by submitting it to them--they get all the rights to your story even if you don't win. They probably will never steal it or ever worry about it, but there's a small chance that if you submit it elsewhere and sell it, they may come after you looking for money. That's probably pretty rare, too, but the only thing I can actually think of to look out for, as far as "theft" goes. As maestro said, I too would stay away from these.
Beyond that, just write.