Magento – Manage categories page does not exist in the admin panel

Delete file from local folder (or rename it to keep changes if you need them). Magento will use original file and there will be no error more.

/app/code/local/Mage/Catalog/Model/Category.php

Edit: Changes to core files being lost in a migration or upgrade can cause this issue. With the benefit of more experience with Magento and @Fiasco Labs comment, my simpler suggestion would be to look for modifications to core files in a project before migration, or really whenever you take over a project. Plugin provider Amasty offers a free tool for checking for modified core files, or you can do it yourself by comparing the "core" folders in your site to those from a clean copy of your site's version of Magento.

Original Answer I'm not sure if this will be helpful to the OP, but maybe it will help someone else. I had this same problem with the catalog product edit page in the admin after migrating our site to a new server.

Based on @Manik's advice, I found that the project had a code file at local\Ourproject\Adminhtml\Block\Catalog\Product\Edit.php that extended the Mage_Adminhtml_Block_Catalog_Product_Edit class. The contents of that file are below:

<?php

class Ourproject_Adminhtml_Block_Catalog_Product_Edit extends Mage_Adminhtml_Block_Catalog_Product_Edit
{
    public function __construct()
    {
        parent::__construct();
        $this->setTemplate('ourproject/catalog/product/edit.phtml');
        $this->setId('product_edit');
    }

}

Because I am not that familiar with how magento paths work, it took some looking around to figure out that I did not have the template file ourproject/catalog/product/edit.phtml on the new server.

I had followed the instructions from the Magento wiki to migrate the site. That process has you copy over your database, create a new clean instance of Magento on your destination server, and then copy over only the files that should have been changed from your existing site.

I suspect that this issue arose because the custom edit.phtml file really should have been created at app/design/adminhtml/ourproject/default/template/default/catalog/product/edit.phtml instead of at app/design/adminhtml/default/default/template/ourproject/catalog/product/edit.phtml, and then would have been captured for migration following the instructions in the Wiki. Someone with greater experience may be able to weigh in on that.

Whatever the cause, bringing over the contents of the app/design/adminhtml/default/default/template/ourproject folder to the new server fixed this issue, and probably a few others I had not yet noticed.