If the new disk is installed on the same server as the old one, boot with your bootable Linux distro of choice from CD/DVD, then you can use fdisk or cfdisk to partition a new disk with new partitions that are a bit bigger than the original disk, and dd to copy your existing partitions one by one . If you do not know what these tools are, then you should not be trying to do this using this method.
You also need to write a new boot record to the new disk. You can also do this using the dd command.
I've used this method to copy a friend's failing Win XP system disk.
There may be other foolproof (Ok foolresistant) ways to do this as well. You may want to google for "clone linux" or somesuch.
OK just had a look, tryhttp://freshmeat.net/projects/g4l/http://www.partimage.org/Main_Page
Also more info herehttp://www.linux.com/feature/152592