My very first digital camera was a Sony Mavica FD-88. It was 1.3 megapixels and recorded the images onto floppy disk. In its day it was a fancy damn camera and cost me a pretty penny.
When using my Mavica, if I wanted someone to take a picture of me the first thing they would do would be to put it up to their face to look through the viewfinder. The camera never quite made it to their eye because they would get a look of confusion then push it away from them again so they could pinpoint the precise location of the viewfinder. This was followed by a look of increased bewilderment because they couldn't find it. Because there wasn't one.
The Mavica used the LCD screen as its viewfinder. You held it away from your face, lined everything up using the LCD (you actually viewed through the lens), and snapped the picture. This may sound familiar because it is the way most pocket digital cameras today work.
I eventually upgraded my Mavica to a Nikon D70 DSLR and went back to having a viewfinder on my camera. I still find it mildly humorous when I hand someone my camera. Because of the increasing popularity of those pocket digital cameras, people are used to using the LCD as their viewfinder. They will stare in confusion at the LCD trying to figure out how to activate it (some even check the lens cap) only to realize moments later that this one has a viewfinder.