What to copy when moving cygwin from one machine to the other?

Yep! Go for it. You won't encounter any problems.

You can just copy the entire cygwin directory to your new machine, open up the cygwin shell and everything (as long as you are only calling cygwin-internal programs and stuff that's within the path) will just work as if you you are working on your old machine.

The only thing you'll loose is the directory where the "already downloaded and compressed" packages for a possible re-installation are stored. Fortunately this directory is optional, so no problem for migration to another platform. You could copy that directory as well, but most likely all the packages that you have are outdated anyways and a run of setup.exe would fetch the new versions anyway...

Btw - since someone said exactly the opposite some real-life experience: I use this feature quite often with success. I've copied my cygwin dir to USB-sticks and used it on friends computers. I also copied it to the laptop of my fiance when we go to holidays and take a laptop with us.

It always worked without any problems....

The short answer is: No, you can't copy the whole Cygwin folder. You just copy the configuration files(bash files, vim file, etc.) you need.

The long answer is: If you copy the whole Cygwin folder, it may work in some case, and may not in some other case.

The reason is: you will lose linux file mode when copying files on Windows. And that will cause a lot of troubles. However, you may not have the troubles when you use Cygwin just like a common Windows Program(which means you don't care file mode and anything related), and run it as Windows Administrator(which is not required when Cygwin is installed as usual).

BTW: you can export the packages you installed by cygcheck.exe -c and install them on the new Cygwin. You can also install/update Cygwin packages by Cygwin's setup-x86_64.exe in command line like:

setup-x86_64.exe -q -P package1,package2,package3