We're liking that LCD viewscreen on our digital cameras, and haven't used that little peephole (isn't it called a viewfinder?) in ages, but sometimes there are good reasons to use the viewfinder instead of the LCD. A little tutorial at the Digital Photography School suggests that the LCD is great for convenience, gives you instant playback, enhances creativity by allowing you to hold the camera at all kinds of weird angles, and helps overcome framing inaccuracy of some cameras' viewfinders. The LCD is also great for those of us who wear glasses.
With all those great reasons, why would you ever not want to use the LCD? Well, for one, it's a drain on the batteries. Plus, you can't hold the camera as steady at arms length, so your shots might not be as sharp when using the LCD, and sometimes sunlight is too bright to even see the thing. And, with some DSLRs you might not even be able to use the LCD as a viewfinder anyway. On the other hand, some lower-end compact cameras have no viewfinder. For us, the LCD reigns supreme, especially if it's a 3-incher.
Should I use the LCD or Viewfinder on my Digital Camera? [Digital Photography School]