That being said, a lot of people don't quite get what this new thing is. It's being billed as a "computational knowledge engine", which is a different thing altogether from a search engine, like Google. This is something that simply has never existed before, which is why so many people are having trouble figuring it out. You can't use it to search for things, like the best value car, or the cheapest cell phone, because that kind of thing can't be computed, except by methods that would either be biased, or not be trusted, or both.
But for things that are computable, Wolfram|Alpha excels. It builds on the computation power and symbolic interpretation of Mathematica, and takes it to an entirely different level. While Mathematica is designed for professionals, Wolfram|Alpha is designed for the whole population, although many of the data sets are rather specialized. As things stand now, this product is only starting. It's at the first point where it's good enough to be used by the public, but it has a long way to go. There's a lot of work to do, and a lot of things won't work, and there's a lot of data that hasn't been put in yet.
So if you run across things that don't work, or that you think should be added, use the feedback form on the bottom of the page. Your feedback will help make it better. I'm not just saying that, either - I'm actually one of the people who reads that feedback, and makes sure it finds its way to the developers. So sending feedback will also help to ensure my future employment. *grins*
There's a lot of articles out there which show off what Alpha can do. I figured I'd show a few examples, myself. So if you'd like to see some examples,
Unsurprisingly, Alpha is best at math. Try the "show steps" button in some of these results to have it do your math homework for you.
Alpha has a lot of excellent geographic data.
Alpha has access to a lot of data about common materials. I'm sure my dad, who is a civil engineer, would appreciate being able to look up things quickly.
It can do lots of conversions, too. No more looking up the conversion factors in your little black book.
And of course, it's particularly good at electrical engineering. As an example, it can crunch Ohm's Law for you.
Alpha can do some very cool things with colors, something I'm sure circe_ravaine will appreciate. Go down to the Related colors pod, click on Show details, and Show more colors. It'll give you a full range of complimentary and contrasting colors, plus a pre-calculated intensity gradient, for any color you want - all with full RGB values.
Alpha has access to lots of current data from the stock markets, and can do some excellent computations and comparisons on them. Want some stock tips?
There's lots more, of course, but the devlopers were kind enough to provide an examples page where you can see for yourself. Just remember, it's not perfect, it's not complete, and there's lots of room for improvement. So send in feedback if something doesn't work the way you wanted, or if the data wasn't available, and people like me will make sure that it gets marked to be fixed.