If you want to go from 32 to 64 bit Cygwin but keep all the packages[1], you might find yourself in a spot where you would like to export the list of cygwin packages and also be able to install cygwin with all these packages again. I will tell you how. Open your Cygwin shell and enter
cygcheck -c -d | sed -e "1,2d" -e 's/ .*\$//' > packagelist
This will simply dump a list of installed packages. To install Cygwin 64 with these packages selected, download setup-x86_64[2] and execute it with the command line parameters
./setup-x86_64 -P `awk 'NR==1{printf \$1}{printf ",%s", \$1}' packagelist`
I finally got this to work but it took me a while to find out - by combining the initial description with tkimva's comment: