Seeing as tablets and phones are getting thinner by the day, why not make a camera the shape of an old Polaroid photo?
Dual cameras on the front and back, a single button, and a touch screen. It’s pretty much a phone minus the apps and connectivity. Why would it exist? Hopefully it would be an inexpensive option like a disposable camera. Plus it would be for people who’d like a nostalgic device.
Besides a micro SD card slot, one (optional) feature it would have is “shake to develop”, where images would slowly come into view, but would appear quicker if the camera is shaken (would require a gyro device within).
Dave's Geeky Ideas 
This is a great idea, but it would have to be very inexpensive (under $50) not to be overshadowed by tablets, which already offer tons more functionality. Even if it were purpose-built to be a better camera (higher resolution pics, easy sharing, flash, etc.), I can imagine most consumers would pay more to have all the features that android tablets/iPads do.
That being said, if a similar device was built and marketed primarily as a camera/picture-viewer, but ran on Android, I think it would be a standout option in the current sea of tablets, many of which are very similar and don’t have truly distinguishing features. As an example, any Android tablet can run eReader software, but the Nook is an eReader that also runs Android apps.
Another thing to remember is that a lot of people have ditched digital cameras for the convenience of their smartphone’s built-in camera, and phones are getting thinner while screens get larger. While I may be straying a bit from the original idea, I would think that this would be most successful if you made a thin, big-hi-res-screen camera that doubled as a phone, but that’s just my 2 cents. 🙂
Plenty of dedicated cameras on the market. Too few cool ones like this (or the other ones Dave made - which are also awesome. I’d love a View-Finder camera!).
i think there’s plenty of room for a cheap, simple camera - while younger audiences might want everything consolidated in a few gadgets, there are plenty of people who don’t use cellphones or tablets and who would really enjoy something fun and snapshot-ish like this.
a couple design suggestions? i’d center the camera lense on the backside - i’m assuming that’s what those two black dots on the white backside are, correct? one is a lense and the other a flash/red-eye protector, would be my guess… also, from an ergonomic standpoint, it’d be nice if this was designed to be held sideways and then auto-rotated the pictures for display - most people would hold this one-handed and using either of the two big buttons on the front as a shutter would be natural placement if the wide edge was clasped in the palm of the hand - holding it upright with one hand while also being able to thumb the shutter doesn’t leave you a lot of room to grip the camera. while i know a lot of camera’s are designed to be held in one hand and the shutter pressed with a second, this is problematic for a number of reasons - least of which just the simple fact most people are going to try to take a one-handed picture at some point, even if it’s just a self-portrait held at arm’s length.
it would also be nice to remove as many of the display icons as possible to leave as much of the screen free for image display - to mirror the original polaroid as much as possible. lastly, ii don’t know enough about screen and material technology to know if it’s currently feasible to build these in a “flexible” model that would accomodate people sitting on them while stuffed in their back pocket - i know we’ve been hearing about “electronic paper”-type screens for a while now but i’m not sure how feasible those are… a super-thin, super-rigid design using gorilla glass or something seems obvious, but i’m just thinking that something with a little flex [about as rigid as a polaroid picture] would really help the product stand out from the rest of the consumer electronics on the market.