Written with an SEO perspective, but still good to refresh yourself with the advanced syntax available on Google. Lots to look at, but here are a few to whet your appetite:
Proximity search. Find pages containing two words or phrases within X words of each other. For this example, the words “apple” and “iphone” must be present in the content and no further than four words apart.
Example: apple AROUND(4) iphone
Convert one unit to another. Works with currencies, weights, temperatures, etc.
Example: $329 in GBP
Find news results from a certain source in Google News.
Example: apple source:the_verge