Hide completed orders from sales/orders

The observer way:

<events>
    <sales_order_grid_collection_load_before>
        <observers>
            <vendor_module_salesgrid>
                <model>module/observer</model>
                <method>filterGrid</method>
            </vendor_module_salesgrid>
        </observers>
    </sales_order_grid_collection_load_before>
</events>

Then in your module/Model/Observer.php

<?php

class Vendor_Module_Model_Observer 
{
    public function filterGrid(Varien_Event_Observer $observer)
    {
        $collection = $observer->getOrderGridCollection();
        $collection->addFieldToFilter('status',array('neq', 'complete'));
    }
}