Anyone that hasn't already done so should browse Google (in depth, might take an hour or more) to become familiar with all the less familiar (new) features.
Google now 'does' Scholar, Calculator, Numbers (patents, FCC ids, etc.), Microsoft-specific (ironic), US-Gov't-specific, Suggest, Video, Zeitgeist (search trends), and so much more. Some are beta and some are quite new.
Of course, there's the tools listed on the front page as well: Images, Groups, News, Froogle, and Local (new). These can be very useful as an alternative to just the WWW.
Digging down into More and Labs will reveal even more features.
Sometimes adding the term .pdf to your search can help to find better quality information in .pdf files.
And of course, there are many other search engines besides Google. Microsoft's MSN Search is new.