To a me as a photographer, the broad question "What camera should I get?" has one simple answer:
A 40 Megapixel Hasselblad that's only $29,999. And it's a limited edition "Ferrari" edition, 1 of 499. It's freaking awesome. This is the camera you should get.
Now that I got that off my chest, we can move on.
I always tell people, that the best camera is the one you have with you. The smallest, slimmest camera that you can fit in your shirt pocket, is better than any sweet DSLR that you left at home because it was too big.
There are so many cameras out there, it's impossible to narrow it down to just one (except the Ferrari Hasselblad) Here are some simple guidelines that can make it feel a little less daunting. For a point-and-shoot camera, don't worry about megapixels. Just about everything now is over 10 megapixels, and anything greater than that, is much more than a small camera can handle. Do not base your choice on whether one camera is 10MP or another is 14MP. If it is a point and shoot camera, you will not notice the difference.
Do you go to the beach, or like to drop things?
Try this: Panasonic Lumix DMC-TS3 It has a Leica lens, it's small, waterproof, shockproof, and costs $375. There are cheaper versions of the similar camera as well. Avoid the Olympus all-weather, I've heard multiple complaints about picture quality.
Are you not concerned about all weather, and want something a little thicker than your shirt pocket, but has more manual controls and shoots RAW?
Try This: Canon PowerShot G12 It also has a hot shoe for an external flash. Nikon has a similar model. I've personally had the rock-solid G9 since 2007. $499
If you like shooting video, and want an interchangeable lenses, but don't want to go with the size and expense of a full blown SLR there are a lot of "mirrorless" cameras like this:
Sony Alpha NEX-5 Interchangeable Lens
These are cool. They have sensors the size of most SLR's= great quality photos, stuffed into a tiny little body. However the protruding lens takes away from the true "compactness" of the body. A friend of mine shot this video with this camera. There are also many brands with similar style cameras. This one is $699
The options are endless. I didn't even get into the traditional looking SLR cameras. Which nowadays can be had starting at $450!!! Like this
Bottom line is get into a camera store, and put your hands on some cameras. You will know which ones are clumsy, and which ones feel right. Just don't be too pre-occupied with megapixels and how far one zooms. If a camera feels good, good enough that you end up taking it with you places, and it makes sense to you, and it makes you take more pictures-- THAT is the camera for you. I'm going to get back to work so I can save up for my Ferrari. if I know I can never have one in my driveway, maybe I can have one in my camera bag...