My time has come!
The above stereographic image is for cross-eyed viewing (most stereograms are wall-eyed, so you may need to put your finger in front of your screen until this one comes into focus)
This is an image of Honolulu, Hawaii, published by NASA. Note Diamond Head (the volcanic crater) in the south.
Here are some other stereopairs published by JPL:
Wheeler Ridge, California
Mount Saint Helens
Salt Lake Valley, Utah
Wellington, New Zealand
They do work. It takes some practice to get them though. At first I used a pencil or something to focus on while I made the two dots merge together, stayed focussed on the pencil until my brain "saw" the image behind it, then it sort of locked in and I could take the pencil away. I've done so many of them now that I can just go crosseyed to bring the dots together, then look at the middle picture.
The 3D image works by tricking your brain into seeing a third image that isn't really there. We're used to constructing 3D images from two slightly different views; we do it all the time, so the two images are slightly different and when overlaid use the same mechanism to make you think it's 3D.