Interesting question..
If you want to shoot in a certain aspect ratio with a specific frame shape in mind, or otherwise for artistic purposes, setting the camera to shoot in that ratio (e.g. the 16:9 mode that many compacts have) will allow you to compose the shot on the LCD and achieve a better-composed result.
But for general photography, I'd set the camera to use the whole sensor available, which means shooting in 4:3 for most compacts, 3:2 in full-frame, etc. Any cropping to achieve a different aspect ratio can be done later in post-production.
I had an experience of this when I wanted to show our holiday pics to the in-laws. I had the idea of cropping them all to 16:9 to fill the TV screen. Some, such as landscapes, were ideally suited to this format, but with others it was difficult to crop them without losing important detail. 16:9 for a photo is wider than you think..
A.