Your responses to my original question were as diverse and interesting as I had hoped for, but they did increase my awareness of just how big this topic is. Though a few book reviews and subsequent editorializing will organize future posts, I thought it might be helpful to begin by trying to think about the natural world in a distinctly Christian way. In no particular order, here are some of my ideas on how to understand it.
The natural world isn't human. It's different than you or me, so we shouldn't treat it like an extension of us.
Nature doesn't belong to us, though we have responsibility for it. Several of the commenters mentioned stewardship. The word stewardship implies caring for something that does not belong to us. My mother pointed out that caring for nature isn't that different from caring for children. Children are given one for a time to care for, but ultimately they are God's. So too, nature is God's, but we have responsibility to care for it for a time.
We are part of the natural world. I think it would be right to say that nature is almost a pseudonym for creation in it's entirety. We are natural, the universe is natural, God's created order is nature.
Nature is bigger than us. Obviously.
Nature isn't only natural. I've often, and I mean often, thought about the rocks and the trees crying out and I don't think it's just rhetorical. I'm going to spend some time writing about nature as a spiritual entity, but for now, let's just say that if it can talk to God when we fail to, perhaps our definition of nature needs to include something supernatural.