As Danny Sullivan reported earlier, Google's Conversational Search is now live on the Google desktop at Google.com.
Basically, it lets you talk your query to Google and Google will respond back with a response, depending on the query. This was a feature available on Google's Android phones and also available via the Google Search App on iOS. It is also like Apple's Siri and similar products. Now, it is available on the desktop.
Here is a video of my playing with it:
As you can see, there is a random bug where Google will return a "no internet connection" error.
This was also reported in a Google Web Search Help thread.
Note, as you can see, it is not perfect. I did have a cold but it does work pretty well.
Forum discussion at Google Web Search Help.