Magento – How to remain on the same page when I click on add to cart button in category page

You need to rewrite the method _addItemToWishList from the controller Mage_Wishlist_IndexController and replace the last line.
Instead of

$this->_redirect('*', array('wishlist_id' => $wishlist->getId()));

You have to put:

 $this->_redirectReferer();

[EDIT].

Here is an example on how you can rewrite a controller.
You need to rewrite (like I said) Mage_Wishlist_IndexController. The controller is found in app/code/core/Mage/Wishlist/controllers/IndexController.php.

There is an option on the add to cart from to submit submit_route_data which will override the standard add to cart url used in Magento.

public function getSubmitUrl($product, $additional = array())
{
    $submitRouteData = $this->getData('submit_route_data');
    if ($submitRouteData) {
        $route = $submitRouteData['route'];
        $params = isset($submitRouteData['params']) ? $submitRouteData['params'] : array();
        $submitUrl = $this->getUrl($route, array_merge($params, $additional));
    } else {
        $submitUrl = $this->getAddToCartUrl($product, $additional);
    }
    return $submitUrl;
}

I have not used this myself but this should work at least for internal urls. An example can be found at app/code/core/Mage/Checkout/Block/Cart/Item/Configure.php in the function _prepareLayout.

For external urls you may need to work with the event controller_action_(pre|post)dispatch_{{fullActionName}} here you should be able to catch the pre dispatch for the add to cart action and then simply redirect the user when the product being added matches a certain product.