If a product has inventory and cannot be back ordered, it would be nice if it stopped showing up in the store front once inventory has been depleted. It should still show up if back orders are allowed on that product, but there should be some indication that it is on back order. So maybe the inventory number could be in red or something with the words "BACK ORDER" or something along those lines.
In response to Jim Riddles comment: Yes, of course. It should be an optional choice. Either the product shows all the time or the discussed option, but the administrator should most definitely be able to configure it either way by choice.
Put it on the product general page right under to the "back order allowed" check box. I have had this request more than once.
agree for the option to enable this
Please note that this should be an option that can be enabled, rather than an across the board rule. We have some customers who always want to see the products on their site, whether or not there is available inventory. Some use it as a reminder to order inventory, and others just want to always see their products.