If I read someone else's scene that describes a situation in my own work if adapted to fit my characters and plot, would it constitute plagiarism if I so use it?
Plagiarism: The act of plagiarizing: the copying of another person's ideas, text or other creative work, and presenting it as one's own, especially without permission.
Technically, stealing an idea is plagiarism just as much as stealing their words. However, as another old adage goes, "There's nothing new under the sun." Everything you ever write is going to be influenced by other things you've read in the past.
Just make sure that the story you're telling is your own, and not somebody else's. Let yourself be inspired by other writers and what they do, but don't go stealing their work wholesale and trying to claim that it's yours.
During college, with my professor's permission, I re-adapted a short story that I'd read to be from the point of view of another character, changing elements of the story. It was a great exercise for my writing skills and proved to be one of the best things I've ever written.
Without substantially changing the story so that the original author couldn't recognize it, I wouldn't submit the story to a magazine or journal. While I'd added characters and modified many pieces, the original story was still recognizable. It was a good exercise, but too close for comfort.
If you feel the original author of your scene would not recognize it, you have probably "owned" the idea enough to make it your own idea. If, however, you have not been able to change it substantially, I would shy away from using it.
You are evidently aware of plagiarism and seem to consider it something that isn't right. In that case, to a certain extent, I would go with my gut feeling. Is what I wrote too much of the original text for my own comfort? Then I have probably stepped over the line. Am I not sure? Well, why not? I should probably reexamine my text. Do I feel that the source text was more inspiration than anything? Probably fine. Of course, you shouldn't take this rule as an excuse to steal, but generally speaking, I find it applicable most of the time.
You will be affected and inspired by books you read, films you see and everything else you take in, whether you like it or not. Probably the best recommendation would be to give credit where credit is due.
You should decide if you're worried about plagiarism or copyright infringement. The first is an ethical concept, the second a legal one. In copyright, you are protecting your rights to the expression of an idea; you can't copyright the idea itself. So I can write a sci-fi story about a rebellious group of pseudo-druidic soldiers taking arms against an evil empire without George Lucas breathing down my neck. I start naming characters Luke and Leia and I'm going to run into trouble.
Plagiarism is an ethical concept, so the boundaries are squishier. Basically, if you think it's plagiarism and can make a decent argument, it's possibly true to a degree, even if that degree is vanishingly small. "My God, your zombie/robot novel has characters! And they do stuff? That's obviously stolen from Agatha Christie!" Unless it's actually copyright infringement, there's also nothing anyone can do about it legally. The only harm will be to your reputation.
Take the Hunger Games / Battle Royale dust-up. Both stories are differing expressions of a similar idea. Even the accusation harmed Suzanne Collins' reputation, but there wasn't a legal redress.