No, do not just throw it away, that is an identity theifs dream to find that in the trash. Some keep their old passports as souvenirs to pull out and look at the stamps from time to time. It can also be used to prove your identity if you lose your current one. If you want to destroy it I would recommend a paper shredder (cross cut preferred). I think you can return it to the passport office stating you marked for destruction.
I will burn mine so I know nobody will get hands on it.
I save my old passporst. Do not just toss it in the trash. If you lose you currant one, you can present a canceled one for identification. If you no longer want to keep it, use a shredder.
We kept our, the government here punches holes in it, but we kept the stamped sections.
I save mine as souvenirs, and look at the various stamps.
My old passport has the two holes punched in it along with the huge cancel stamp. I will shred it. Thanks guys.