Stereograms take a little practice to get the hang of, but afterwards are very easy to see almost at will. One trick is to focus to a point far in the distance, looking through the stereogram, and slowly pull your focal point closer. Using this method you will sometimes see a double-vision version of them that you can then focus into a single version. Once you start to see the hidden object, the rest of it comes together in a couple of seconds.
One of the others on the site you listed uses the same design for the 3d object and the pattern. Look at http://www.eyetricks.com/3dstereo24.htm
the hidden object is a big version of the little crossed circles. When you have it properly focused, there will be 6 white circles in the forground, then the large hidden circle, and finally 6 green circles in the background. The little ones overlap the big one so that inside each bottom quarter of the large one is one of the little green ones.
Hope that makes sense. 
Below are some of the easier ones to see. http://www.eyetricks.com/3dstereo40.htm http://www.eyetricks.com/3dstereo7.htm http://www.eyetricks.com/3dstereo29.htm http://www.eyetricks.com/3dstereo17.htm
[This message has been edited by EMatthews (edited March 12, 2002).]
[This message has been edited by EMatthews (edited March 12, 2002).]