I have an web server with CentOS 6.7 installed. Now I aqquired a new computer and want to make it to run the web server but it is hard to fresh install and copy all the content (hundreds of websites). Can I move the hdd from old server on the new server? And if something does not work can I switch the hdd Back? Is there any risk? Both are 32 bit systems. Thanks!
Taking your questions in order: almost certainly, yes but I can't gaurantee no difficulty, probably low but yes. Obviously there is the issue of driver support for the new machine's hardware. You'll need to figure that out.
Therefore if this is very important I think a safer solution would be to clone the hard drive to another physical disk with a tool like
dd. Any Linux livecd would suffice to do this, but a specialty tool that offers at least some handholding is partedmagic. You'd need a disk the same size or larger. A USB SATA dock like this and some drive cloning software might be another option. The dock could save you trouble either way by just letting you plug your HDD into the dock instead of having to open your old computer up and physically connect it before repeating on new computer.
You don't even need to physically remove the old disk to do this. You boot your livecd or partedmagic and a command like
dd if=/dev/sda of=/dev/sdb bs=64K conv=noerror,sync
where /dev/sda is the old disk and /dev/sdb is the new disk should do the trick.
If you get a larger disk, a tool like gparted would let you resize partitions (you'd probably want to adjust your swap partition, and use up any extra space the new HDD offers). Again, to do this initial configuration you'd probably want to use partedmagic or any livecd with gparted because you can't really monkey with a live operation system in most cases. That being said, depending how you set up CentOS, CentOS itself might make partitioning and resizing very easy and straightforward.
Also, as IMHO 32-bit is getting ever less current and relevant, maybe it's time to just take the plunge and set up a 64-bit OS? (You don't say what hardware you're using. But PC hardware generally may as well all be 64-bit nowadays.)