You can remove the hard drive and put it into an external case, however, yes, hard drives have changed too. The most common external case will have a SATA drive interface. This drive will require a PATA drive interface.
So, what you'd be looking for is:
3.5" USB2 External hard drive enclosure for PATA hard drive.
NOTE: PATA used to be referred to as 'ATA' or 'IDE' but is now more commonly referred to as PATA to distinguish it from SATA, the new interface.
The enclosure will require it's own power supply - this may be an internal power supply (with a mains cable to connect) or an external power brick.
The only other problem you may run into is your document compatibility with newer programs. For instance, old ClarisWorks documents would need to be converted to work with modern word processor software. That requires a machine capable of running Appleworks version 6, which again will be an older machine now.