Apple iPhone 3G 
Beginning with the hardware; it doesn't focus or zoom. You have no control over the exposure. The resolution is pathetic, image quality is nothing like as good as my first digicam from a decade ago, there's horrible noise to contend with, no flash when you need it, no macro or sports mode. It is what it is; a low resolution, fixed focus auto-everything digital camera - it is, in fact, most of what I dislike about digital photography.
So why is it so popular?
Beyond the Emperor's-New-Clothes syndrome there is The Best Camera effect. Jase Jarvis wasn't the first to propose that the best camera is the one you have with you but he did apply the philosophy a little differently than those who went before him. I always took it to mean that you should always carry a camera with you so you have it to hand when you need it. Chase Jarvis took it to mean that you're already carrying a camera around on your iPhone so why don't you use that ... and while you're about it you can buy his application and book, visit his forum, become a fan on Facebook and follow him on Twitter.
There are other apps you can buy to disguise the fact that what you're using a crappy camera phone, making it look like a Polaroid (ShakeIt), or Toy Camera (Hipstamatic), or countless other variations. Most of these apps have some cookie, slow interface that will crop your image square (because it's hip to be square kids), apply a filmic border, boost contrast and saturation then apply a vignette and some scratchy, mucky cross-processed, layers to complete the illusion all without you having to do a thing but press the virtual button. Upload it to Flickr where people rarely look at you pictures in higher resolution than the thumbnail and no one will be any the wiser.
My wife berates my kill-joy attitude and tells me just to have fun with the iPhone and to stop being so serious. I would but people are building careers, fortunes and reputations based upon these snaps and apps. If it gets people fired up to get into photography, great, but if their happy accidents based upon some random algorithm deliberately built into their phone's software get compared with someone really in control of their art and craft then I get upset.
That's not to say that the iPhone's camera is worthless; it is great for visual notes (where did I park? which wire went where before I took my PC apart?) You can even coax a decent picture out of it with a little care. My favorite way is to create panoramas out of iPhone pictures; this allows you to compensate both for the cameras limited resolution and it's fixed focal length. Still, the end result is more 'acceptable' than 'great' so don't leave your real camera at home now you have an iPhone.
Maybe, when my current contract ends and the 4G is out with a better camera on board then I'll eat my words. Until then I'll save my iPhone's camera for disposable snaps and leave the photography to a real camera.