A typical home computer hard drive can contain your credit card numbers, bank account numbers, and website logins and passwords. This information can remain even if "erased" or reformatted.
When disposing of an old PC, there is really only one way to securely erase the information on the hard drive: You must destroy the magnetic platter inside.
Use a T7 screwdriver to remove as many screws as you can access. You'll probably be able to remove the main circuit board from the enclosure.
You probably won't be able to get the enclosure open with the screwdriver alone. That's where our hammer comes in...
With your eye protection on, repeatedly strike the hard drive on various sides until it starts to open. When open, you want to coax out the round silver platter from inside.
Seriously, BE CAREFUL! Hard drives contain all kinds of parts that can go flying, even if you're hitting it somewhat gently. Older hard drives can even contain glass.
You don't need a lot of force to get the drive open. Several lighter hits are better than fewer heavier swings (and safer, too). You just need it to separate enough so you can peel the top back.
Ding, dent, and scratch this platter. You don't need to swing like an axe murderer, many lighter taps with both the claw and peen of the hammer should destroy the hard drive sufficiently.
When done, box up all components and turn them in at your local electronics recycling center.