I had the same problem with Anaconda3 4.2.0 and 4.3.0.1 (64-bit). When I tried to run a simple program that uses matplotlib, I got this error message:

This application failed to start because it could not find or load the Qt platform plugin "windows"

Reinstalling the application may fix this problem.

Reinstalling didn't fix it.

What helped was this (found here): Look for the Anaconda directory and set the Library\plugins subdir (here c:\ProgramData\Anaconda3\Library\plugins) as environment variable QT_PLUGIN_PATH under Control Panel / System / Advanced System Settings / Environment Variables.

After setting the variable you might need to restart PyCharm, if the change does not have an immediate effect.

Even though after that the command line Python worked, TexWorks (which uses Qt as well) displayed an error message very much like it. Setting the QT_PLUGIN_PATH to the directory containing TexWorks' Qt DLLs (here C:\Users\chris\AppData\Local\Programs\MiKTeX 2.9\miktex\bin\x64) fixed the problem for both programs.

If you are running PyQt5 and PySide2, this solved the problem for me:

Copy the following files:

\Anaconda3\Lib\site-packages\PySide2\plugins\platforms\qminimal.dll
\Anaconda3\Lib\site-packages\PySide2\plugins\platforms\qoffscreen.dll
\Anaconda3\Lib\site-packages\PySide2\plugins\platforms\qwindows.dll

to:

\Anaconda3\Library\plugins\platforms\

I found that this was being caused by having the MiKTeX binaries in my PATH variable; and the wrong Qt dll's were being found. I just needed to re-arrange the PATH entries.

(Dependency Walker is such a useful tool.)