How can I easily transer all the packages I have downloaded with apt to another box which is not connected to the internet?

sudo apt-get install apt-move

(Or just use synaptic) You need to enable the universe repository. See AddingRepositoriesHowto

sudo apt-move -d breezy update

Because ubuntu repository structure, not all packages are inserted into the Packages.gz file by apt-move. We must remake the Packages.gz file.

cd /mirrors/debian/dists/stable/main/binary-i386
sudo dpkg-scanpackages ../../../../pool/ /dev/null > Packages
sudo mkdir /mirrors/debian/.disk
sudo echo "Custom packages" $(hostname) $(date +%y%m%d) > /mirrors/debian/.disk/info

Then, using nautilus-cd-burner burn the contents of the /mirrors/debian folder to a disk.

Insert that disk into the non-networked computer and add the cdrom as a repository using synaptic or run

sudo apt-cdrom add

from the command line. When installing the packages from this cd, you will be asked if you want to install these packages without authentification. For the sake of simplicity, the GPG keys and the release file are not included on this simple packages cd. The packages will be installed without any problems if you answer yes.