Wolfram Alpha is live, albeit a little unstable. A couple times I was told "I'm sorry Dave, I'm afraid I can't do that" and shown a live view of the W|A command center, a quiet room filled with monitors of colorful maps and charts and, yes, a dias in the back upon which Stephen Wolfram himself sat at what looked like an old CRT monitor.
It's easy to find queries the system can't process, but it has a surprising amount of functionality - even comparing apples and oranges (with nutritional information!)
One thing that surprised me was that the system displays projected stock paths - see here for the S&P 500 and here for IBM, AAPL and MSFT together. Seems a little bit of a gimmicky thing to feature so prominently... the paths are disclaimed as simulated log-normal random walks based on "historical parameters", which I assume means drift/volatility.
I enjoyed the Black-Scholes page, full of graphs of all the different greeks, and a working option calculator.
Another nice feature is that clicking any graph or table will pop up a plain text version, convenient for copying data.
The full list of categories it can act on is impressive4 twenty-sided dice, or the number of homeruns hit by the Mets in 1993. I was surprised when I asked who wrote The Time Traveler's Wife and was given data about the upcoming movie - although it does claim that August 2009 is a quarter year ago rather than in the future.
On the whole, an extremely powerful calculation engine, as promised. It remains to be seen if this becomes part of my daily use as opposed to a novelty toy/bet settler, but I have a feeling it will. Certainly, the mathematical component and historical data is exceptional; the incredible amount of additional functionality is bonus.
Around the web, early reviewers seem to be faulting the system for either 1) it's inability to draw non-structured information from the web and 2) it's inability to give superspecific data subsets, like zip-code level detail. It seems silly to fault a system for being "less than perfect" while it has already achieved a higher standard than any other, with much room for continued improvements. Where is the praise that the system can do what it is currently able to do? Why are we looking this gift horse in the mouth?
That said, my one hope for improvement is the site's internal search engine - it does not have a good disambiguation system, so unless you type exactly what you mean, it's unlikely you'll get it. A display of topics potentially related to your input would be immensely useful.
Congratulations to the Wolfram Alpha team on a successful launch and excellent product!