Despite the easy peasy button that says "allow backorders" on Magento Ecommerce's backend there are a couple problems when you do this.

For instance if the product says out of stock the checkout button won't show up. So here is a fix for that...

Around line 62 on view.phtml under app/design/frontend/base/default/template/catalog/product remove the if saleable lines surrounding this

The next problem you will find is after clicking checkout there is a red box that pops at the top saying that the product is out of stock - stopping you from moving further to actually put the items in the cart. Here is the fix for that...
Under code/core/mage/cataloginventory/model/stock/item.php comment out the following items

Thats all there is to it. You should now be able to check out products listed as out of stock.