Took a hard disk and network card out of a client's machine and built a new computer around them. Was 200-MHz K6, now 1200-MHz Athlon. No problem whatever (of course I had to set video to VGA and reinstall video driver, but no other changes).
Don't try this with Windows.
I was pretty sure it would work OK, because I did a 233-MHz to 1200-MHz upgrade for the same client a few days ago, and that machine has been in production for a couple days now.
Why didn't I use a new hard disk? Why bother. The client is paranoid and doesn't allow anything to be stored except on the server where it gets backed up to tape - and to the backup server - every night. So the drive only had a few hundred Megs used, and performance isn't an issue since just about everything happens over the network. Even with my totally "follow the dots" installation procedure it takes about 5 hours and a site visit starting with a blank drive.