On MacOSX, by combining the answers from Calaf and Ollie Ford, the following worked for me.
On the command line (be sure adb is in your path, mine was at ~/Library/Android/sdk/platform-tools/adb) and with your android device plugged in and in USB debugging mode, run:
adb backup -f backup com.mypackage.myapp
Your android device will ask you for permission to backup your data. Select "BACKUP MY DATA"
Wait a few moments.
The file backup will appear in the directory where you ran adb.
Now run:
dd if=backup bs=1 skip=24 | python -c "import zlib,sys;sys.stdout.write(zlib.decompress(sys.stdin.read()))" > backup.tar
Now you'll you have a backup.tar file you can untar like this:
tar xvf backup.tar
And see all the files stored by your application.