"Mathematica" is an excellent, stunning piece of software. And "A New Kind of Science" is even more ambitious a project by Stephen Wolfram, to put it very nicely.
But these two things are nothing compared to Wolfram|Alpha, a computational knowledge engine that unifies the previous two revolutionary paradigms.
In two months, the first letter of the Greek alphabet is going to be confiscated by Wolfram Research and it will become a new CML, the Central Brain of Mankind. :-)
Once you'll be able to open www.wolframalpha.com, it will be ready to convert every question of yours, formulated in a natural language, into a well-defined computational format that represents the natural language.
The Central Brain of Mankind will search all (so far only millions of lines of) possible algorithms, methods, statements, and all (so far only trillions) of curated data that exist on the Internet, combine them and recombine them in all conceivable ways, and answer your question. You bet that it sounds amazing enough for me to get excited.
At 4:12 you can see that on May 20th, 2484, i.e. 475 years after the introduction of first Wolfram|Alpha, the Central Brain of Mankind announces that the Earth is going to collide with an object. The world government has to send a few people, in Expedition Adam 84, back in time to 1984 in order to find a notebook of Adam Bernau, an 11-year-old Czech boy who would later win the Nobel prize (yes, I was born in 1973), that explains how to easily move continents from one place to another. They have to save the notebook before it's burned in their family house fire.
Many of us will eagerly wait whether the relevance of Wolfram|Alpha for the real world is going to be closer to Mathematica or A New Kind of Science! ;-)
Via Wolfram Blog. See also Rudy Rucker's interview with SW.
Update: May 2009
See presentations and videos about Wolfram|Alpha getting ready.