This thread is misnamed. If it's supposed to be about psychology experiments, which it seems to be so far, it should say so. A "thought experiment" is by definition something you don't actually do, either because it's wildly impractical - for example, it would involve somehow harnessing all the energy in the Universe - or because it's completely pointless. Shrodinger's Cat is an example of this, because although the experimental setup is quite simple, the bizarre result you're trying to observe - a cat which is simultaneously alive and dead - vanishes whenever you try to look directly at it, so you can never actually see it (there are also at least two other reasons why this experiment can never succeed).

Thought experiments are useful because they allow you to mentally explore aspects of science which can't be directly tested without worrying about your inability to do so, which may lead you to discover things which can be tested after all, thus indirectly confirming what you thought in the first place, or may reveal huge logical problems suggesting that your theory is broken. Some of general relativity's predictions about gravity have for the past century been a borderline thought experiment, since gravity is very hard to study because it's such a weak force, but have been assumed to be true because all the testable predictions work out just fine. However, in the next few years, we'll be launching satellites which can do the experiment for real. If they get the expected result, Einstein posthumously becomes officially even smarter. If they don't, Einstein is still very smart indeed, but there's a peculiar gap in his theory which the next generation of theoretical physicists will need to fill somehow, but that's OK because they like a challenge.

Superstring theory, in which the Universe has many extra dimensions but only over ridiculously short distances, is taken very seriously because if you take it to be true it solves a lot of problems, but it's definitely in the realm of thought experiments for the foreseeable future and probably forever, because unless science is completely wrong about a great many things, there's absolutely no way to test these ideas directly without building a machine similar to the Large Hadron Collider, only with a circumference the size of the the orbit of Neptune. But by assuming the Universe is 11-dimensional in a really subtle way that doesn't show, problems can be solved that otherwise couldn't be.

The interesting thing about this theory which we'll almost certainly never actually be able to test is that it doesn't need to be literally true to work. Quantum physics is so weird that "quantum weirdness" is a perfectly serious scientific term, and we're talking about the next level down, so the truth may be completely unimaginable by humans. But a mathematical model which approximates that unimaginable truth does the job pretty well. And since all those extra dimensions, assuming they exist in the first place, only matter over distances smaller in relation to the diameter of a proton than a proton is in relation to the solar system, whether or not we're 11-dimensional doesn't have any practical consequences whatsoever, so don't expect to turn into Doctor Manhattan any time soon.

So, if the thread title isn't a misprint, superstring theory is my favorite thought experiment, mainly because I'm impressed by the sheer audacity of those versions of it which suggest that everything is 10-dimensional apart from gravity, which radiates across the 11th dimension, losing almost all of its strength in the process, therefore there's a parallel universe where everything is insanely heavy that you could get to (a bad idea, since you'd instantly be squashed flatter than all previous definitions of flat) by moving less than a tenth of a millimeter, if you could do that in the 11th dimension. Which is 6 more dimensions than Mister Mxyzptlk knows about, so it's a good trick if you can do it!