First, Wolfram Alpha is not a search engine. You can not enter terms like "Web 2.o" or "whiteboard" and get website results like Google, Yahoo or other search engines. What this site does is bring you "Conceptual Knowledge." From their About page:
"Wolfram|Alpha's long-term goal is to make all systematic knowledge immediately computable and accessible to everyone. We aim to collect and curate all objective data; implement every known model, method, and algorithm; and make it possible to compute whatever can be computed about anything. Our goal is to build on the achievements of science and other systematizations of knowledge to provide a single source that can be relied on by everyone for definitive answers to factual queries."
So what does it do? If you need scientific calculations or comparisons, especially for students doing research. This is the place to go.
Let say you are having your students investigate nutritional information for local restaurants. Type in "Big Mac Whopper" and you will be presented with the nutritional information (in the typical label format) for comparison.
The site is also great at calculations. Enter "x^2 sin (x)" and the engine will compute the answer for you, no fancy calculator needed.
Enter the name of a city and you will get its current population, location, current weather conditions, time and elevation.
There are a few downfalls. Lets take the search for city. There is one related link to Wikipedia. This is the case for most of what is searched. Also if you don't get the search terms just right the engine will assume, sometimes incorrectly, what you meant and return results for you. For example I used the term "news" and the engine returned stock quotes and business information for News Corp.
Your students doing research on planets? Do you need detailed scientific information on the binterong? The site is great for facts. It should be the first stop for finding factual information on a wide variety of topics. However, it should not be used for general search, and that is not its purpose.
Is it a Google Killer? Probably not. Does it do a better job at calculations, comparisons, and simple facts than Google. Yep! So use it wisely. Oh and if you are looking for something funny, type in 88mph or Where Am I, or Who Are You and see what the engine comes up with....so head on over to Wolfram Alpha and see what you can compute!
Wolfram Alpha Conceptual Knowledge Engine