It's not really possible without a few major hacks and tricks.
What do you need it for? Anything that uses Safari, Mail, Push Notification. Numerous apps need it, like MLB At Bat, AP Mobile News, NY Times, USA Today, ABC News, YouTube, anything Twitter, Facebook, any games that develop online gameplay.
Despite all of that, yes folks, there are people who would love an iPhone without all of that other stuff. My mom has said as much. She would use it for making phone calls, having all those addresses, maybe keeping up with a calendar (believe it when I see it), and using it to store photos. I can see her using the camera function as well, although she carries around a P&S camera in her purse that's way better than any mobile phone camera.
I have heard and seen that the Samsung Eternity does pretty much this. If Apple can create an iPod shuffle that is sucked of features, then Apple can do the same with an iPhone and market it to the baby boomer generation. I think my grandma could've even used one of these because of how huge the numbers are compared to any non-touch screen cell phone.
Yes, most of us on here will use our data like crazy. But there is a huge segment of the world that could care less and just wants an easy-to-use phone.