Philipp has a great list of tips, which Tara distilled and then she added her own comments. Great stuff.
Here’s a tip that I haven’t seen mentioned yet. You know that you can use site:gov or site:ac.uk to search over the contents of a top-level domain, right? For example, you can do [site:ac.uk mp3] to look for pages with the word “mp3″ on UK university pages.
But did you know that you can also use the site: operator with subdirectories? For example, the search [site:apple.com/support calendar] will restrict the search for “calendar” to pages on apple.com/support. Or [site:channel9.msdn.com/wiki dhtml] will search the wiki subdirectory of channel9.msdn.com for the word “dhtml.” This has been something I’ve wanted for a while, even though I could always use inurl: as a workaround to get the same behavior. After I noticed that MSN has this ability (Chris Payne, you’re a Kentuckian too, right? Kudos!), I stopped someone and asked why our site: operator didn’t work with subdirectories. “What are you talking about?” was the reply. “We’ve supported that for months--didn’t you notice?” Oh well. I’ve been wasting keystrokes with inurl: for a little while, so I wanted to mention this to you. 
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That is great advice!
I have also had some good results with the command: [site:.edu Keyword] and this will pull up only educational sites that have your keyword in it. Very useful when searching for an academic explaination and sifting through the commercial sites. Ironically I have also found some “perfect fit” sites to include links to and from my site with using this method.
btw, congrats to Google on their alliance with Sun. I’ve been waiting for you guys to give MS a run for their money
ps. Any chance someone could look into making the G toolbar Autofill feature work with ASP.NET forms?
I didn’t know about the sub directory thing, that’s really interesting and useful to know.
This is a nice shortcut, but in certain cirumstances [site:domain.com/dir] returns a different set of results than my old standby [site:domain.com inurl:domain.com/dir]
I’m not sure exactly what’s going on, but it seems to mostly affect queries that return a large number of supplemental results. Wierd.
Nice feature. Now you need to add to the following to the GTB search dropdown…
[G] Search V
….
Current Site
Current Directory and Below
….
Dave, I’ll check on that. Maybe the supplemental index doesn’t support that type of site: search yet. Thanks for mentioning it.
That’s a big list and very well explained, thanks matt