you could always tar and bzip/gzip but you'd need space to save the the copied files to first.
The over alternative is to back up to a removable HDD if you've got hundred(s) of gigs to back up this would seem more sensible as even if you compress the data its gonna take up a few DVDs to store it.
My friend got one of these and hes really happy with it though it comes preformatted with NTFS so if your gonna use it with GNU/Linux you will probably want to reformat it (using fdisk, cfdisk, gparted etc) to ext3 or sommit.
the process is then just a case of copying across but I would suggest using rsync rather than cp or whatever you normally use.
you could also cycle directories every other week
rsync -av /home /media/NEWHDD/Back_up_Home_A/ - one week
rsync -av /home /media/NEWHDD/Back_up_Home_B/ - the next week.
rsyncs great cos it only changes files which have changed it will take longer than cp the first time but after that faster. It also works well over a network so if you set up a backup server then you could set up cron to do it when your asleep and just forget about it
Using the -z flag will compress the data on the fly check out full details at http://www.samba.org/ftp/rsync/rsync.html or by typing man rsync into a shell