Suppose you have a nice install of Ubuntu on 32bit P4, and you are moving to a new 64bit Quad core. This precludes the possibility of using something like remastersys backup since the architecture is different. The OS can not be put on the new hardware.
get a list of the currently installed packages
dpkg -l
lists installed packages and a short description, including versions
dpkg --get-selections
a list without descriptions or versions, useful for dumping back into dpkg on the new machine
For example, on the old machine do
$ dpkg --get-selections
then on the new machine,
$ dpkg --set-selections < installed-files
backup Firefox using FEBE
backup /etc/fstab
backup ~/.bashrc
backup matlab licence, /opt/licenses/licenses.dat
download a copy of the latest Ubuntu ISO and burn to disk