I use EXIF data constantly to figure out why a photo did or didn't turn out right, especially when taking night photographs. This data can tell us nearly everything we need to know from the camera model that was used down to the individual settings. Settings are useful, of course, for determing the causes of anomilies. Or, just as importantly, what was not the cause, meaning a blur wouldn't be likely when the settings were very quick. The camera model is useful in determining the quality of optics - many camera models are prone to "artifacts" - and in determining the capabilities of the camera to help improve the pictures.
Many common programs have EXIF viewers with plugins to ie, firefox, and explorer, but to make things easier I'll just link a free viewer I use. It's called EXIF Pilot Light (windows 98/xp/vista) and can be safely downloaded here. The perks include full exif data instead of just the basics, a thumbnail viewer, and the ability to click the photo and preview the full version in windows explorer. The only thing I don't like is that you can't copy the exif data... boo. But it's better than the photoshop viewer.

Pretty basic. Directories on the left. Find where your photo is. Click it, you get a thumbnail. The default is the basic file information on the right. See the EXIF button under the thumbnail? There's the good stuff, click that.
The camera settings are too complex to even begin with, maybe some of the others would like to get started on that but I'm not that motivated yet. Either way, here is a great beginner's tutorial.
I'm only scratching the surface here, would love to hear more input!
