For instance, I took this picture when I was in vegas, I had just walked into the hotel. I was first able to get the shot at all because of antishake, its dark in there. Secondly due to the long shutter the people are blurred, showing the activity and motion in the lobby.
Perhaps at iso1600 with a fast f/2.8 lens I could have gotten a sharp shot without IS/AS, but there would be no motion blur. With a tripod OR with AS you can get a sharp shot with a long enough exposure to show motion. Works very well with flowing water too since 1/30 is about the best (IMO) shutter speed.
AS works as a replacement for a tripod in a few boarderline cases, it just gives you some extra flexibility and options... which is what buying 'better' equipment is all about.