In many respects, LCD screens are what make digital cameras possible. After all, you need something like a computer screen to read the complexity of a computer output, which is what the plethora of menus and options on digital cameras have become.
Beyond pure necessity, they're also more convenient for many people. Instead of squinting one eye into a small hole that doesn't show you quite the image you'll be getting, you see things on a big bright LCD screen that you can even use to show other people miniatures of your photographic creations. Furthermore, LCD previews increasingly provide a more exact version of your image compared to viewfinders, especially with regards to techniques like manual focus for macro photography.
So, it should be somewhat unsurprising that many photographers, particularly casual ones, refrain from using viewfinders in favor of the LCD screen. Camera companies have picked up on this, and now many cameras don't even have viewfinders, and those that do tend be of relatively poor quality with little effort put into their development. Many professional photographers have begun to complain about the decreasing quality of viewfinders in DSLRs, pointing particularly to the decrease of coverage that the viewfinder provides relative to the picture you'll actually be taking, and the amount of magnification in the viewfinder itself. Little development has been put into creating usable electronic viewfinders that average consumers might at least be tempted to try, and quality optical viewfinders are an increasingly expensive rarity.