For instance, when looking for information on the new economic stimulus tax rebate thing, a search for "tax rebate site:irs.gov" gives much more direct information than does just searching for "tax rebate." Which is great if you know the domain to which you'd like to limit your search, but yesterday, I didn't.
Someone was looking for information on the James Madison dollar coin, and the U.S. Mint website seemed the most logical place to look for it. However, I didn't know the Mint's domain name. So before my usual site-specific search, I first searched for "us mint" to get the domain, and then I was going to run a second search limited to that domain.
But Google is one step ahead of me (I don't know if this is a new feature or if I just never noticed it before): my search for U.S. Mint returned the Mint's website as the first result, and the listing included a site search built right in to the search result (see picture).
I'm generally skeptical of Google as a company for hording private data, but they do have smart people working there.