Generally speaking, you never want to just throw a computer hard drive away. The files on there, even though they may be very old or seemingly harmless, can give away a lot of information about you. Just formatting it isn’t enough (it’s actually quite easy to recover files from a formatted drive). Breaking the thing isn’t sufficient either: the data can still be read from the shards of those magnetic platters.
Now, whether anyone might want to take the time to reassemble those shards and go to the effort for you is another discussion. But if you want to be sure your data can’t be recovered, he’s how to go about it.