Yes you can… fix your iPhone and Touch
If you one hop your iPhone or Touch, you will most likely pick up a device that is fine. I have actually been amazed at some of the bounces our devices have survived. One time in the line to put my things in the airport security bins my iPhone tumbled out and walked all the way past the security scanner. On the other side we had a phone drop from knee hight and we picked up it up with a broken screen.
If a break happens in your future, there are a few options. Best Buy has a Warranty option. Apple offers replacement on manufacture defects. Otherwise, you can buy a remanufactured device with trade in for a little off of buying a new. You could always buy a new device and extend your ATT service contract.
In the case of a broken screen… you could replace it yourself. The parts, the tools and the instructions are all readily available. You will be working with sharp little pieces of broken glass, little connectors, little screws, tight rubber gaskets, and… well, you get the idea. Apple wont be accepting the device back as a trade in if they think you opened the device. All these negatives, why would anyone risk it? Apple previously loved replacement units are around $250 vs a replacement screen is $69.