If you've got a hard drive and it's being written to, just turning off the computer can damage your files, even on an Amiga. Usually on an old Amiga there aren't a bunch of background processes running which are writing data, so you don't need to go through a formal shutdown to tell all those processes to stop writing and die. If you do though, or if you power off while some program is writing stuff to disk, you're going to have some garbage on your drive.
