When Apple released the iPhone 4, they also released a proprietary case for the phone. They call it a bumper. It is basically a stiff band of plastic and rubber that form-fits around the edge of the phone. It's priced (for now, anyway) at $29. I bought one. Here are my thoughts after one day:
It's about as unobtrusive as any iPhone case could possibly be. Doesn't affect pocketability, unlike just about every other case I've ever used or seen.
If you buy it in black, it's mostly invisible.
The button caps they built into it are really nice: the volume up/down and sleep buttons feel and work exactly like the actual buttons on the iPhone. (But see below for warnings about the vibrate toggle button and the dock connector.)
The case is very likely to protect the glass (front AND back now, mind you) on drops. I'm skittish about this since I broke the glass screen on my iPhone 3G—granted, it was on the 50th drop or so, but still.
It will definitely protect the metal edges, which are also the antennae, from scratches.
It allegedly alleviates the reception problem that some users experience when bridging the gap in the frame/antenna. I can't test this easily because I hardly ever see the problem, but the science of it makes perfect sense.
The material of the case makes it grippy against both leather and fabric, so it's safe(r) to set the phone on the arm of your couch. (Previous iPhones were spectacular on leather and "oh crap no!" on fabric. The iPhone 4, naked, is iffy even on leather.)
Unlike the other buttons, the vibrate/toggle button is accessed through a hole in the case. I don't know any way around this, but it's buried so deep in there that you have to get your finger at nearly 90° to the phone in order to flick the button. It's impossible to turn silent mode on or off without taking it out of your pocket. Since I want to do this about ten times a day, I find it nearly a deal breaker.
Whereas the iPhone 4 itself is pretty much impervious to dust, the case will catch dust and hair and stuff. Cleaned out easily enough by removing it and giving it the old "Blades of Steel" treatment, but a bit annoying.
The 30-pin dock connector (a.k.a. "where you plug it in at the bottom") is accessed through a recessed hole in the case. Works flawlessly with Apple's cables, but the Belkin charge cable that I use in my car doesn't fit through the hole, so I'll have to bring an Apple cable along with me. Other third-party accessories may present more or less of this same problem.
Even with its minimalism, this case does change the look and feel of the iPhone 4. When I take it off to clean out the dust, I always think to myself, Oh man this thing looks so cool without that case, and it feels better in the hand too. So far, I've contained my vanity and put the bumper back on after a few minutes.
The Overall Rating:
Somewhere between "Recommended" and "I'm Going to Return It." If you have serious reception issues, it's definitely worth the money. If you are on the fence about a case at all, or if you need a case but can tolerate a bulkier solution, it's probably not. I'm sort of in the middle, so I'll keep it for now.