Where to put plain object classes?

What? I don't know what you have done but you don't need to include anything to use a model!

You are incorrect, sir! If you want to extend CI_Model, you must either
a) include/require system/core/Model.php explicitly
OR
b) call $this->load->model() to get CI to require/include the CI_Model class for you.

To prove, try downloading a fresh CI3 from here:
http://www.codeigniter.com/download

Edit the Welcome controller so it's index function looks like this:

Code:

public function index()
        {
                require_once APPPATH . "models/Testmodel.php";
                $v = new Testmodel();
                $v->foo();
        }

And create a Testmodel class in application/models/Testmodel.php that contains this:

Code:

class Testmodel extends CI_Model {
  public function foo() {
    echo "congratulations! foo is running\n";
  }
}

The result:

Code:

Fatal error: Class 'CI_Model' not found in /path/to/CI/application/models/Testmodel.php on line 2