grattman
In most cases you can remove a disk from one server and install it in another server (with different hardware) and it will boot up OK. Linux will find the hardware & load appropriate drivers at boot up time.
This should be OK for Pentium to Pentium systems or AMD to AMD systems etc.
If necessary you can run the CD install (but select the upgrade option) to install new kernels etc for different processors, without losing existing data etc.
If you have RAID1 system, you can pull out a drive and install it in the new server, and then increase the disk size using this method.
http://wiki.contribs.org/Raid
See Upgrading the Hard Drive Size
Note that if using clone software you need to ensure it supports RAID & lvm etc which many don't.
I want to put a word of caution on this!!! If you have a RAID 5 setup (3 HDD's or more), and they're mixed (I don't know what happens to the same drives - in my case I have 2x SATA & 1x IDE HDD's), and you move them over to a different machine, chances are the RAID will fail completely. This happend to me when I wanted to move from an existing server to a different one (Mobo, CPU, RAM & Chassis was different). Luckely I have backed up the machine prior to the HDD move (even though I didn't think it would have failed).
I do think it has something todo with the HDD order in the RAID stripe set, but I guess when you move a lot of HDD's, you don't take note of the order, and especially the controler order. I think on the 1 PC the IDE was initialiased before the SATA, and on the other PC the SATA is in compatibility mode (different mobo's, different settings / options), so this could play a role as well?