Advanced Operators
Google supports several advanced operators, which are query words that have special meaning to Google. Typically these operators modify the search in some way, or even tell Google to do a totally different type of search. For instance, "link:" is a special operator, and the query [link:www.google.com] doesn't do a normal search but instead finds all web pages that have links to www.google.com.

Let's say I want .edu pages about Mae Jemison. Google now allows the following search:
allintitle:"mae jemison" site:edu
Once you've gone past two syntaxes you have to be careful what syntaxes you use to do the searching. allintitle: and allinurl: can cause search errors. Instead, use intitle: and inurl: instead. I've found in my experimenting that they work much better. This query actually works now:
intitle:mae intitle:jemison inurl:mae site:edu nasa

This also answers my complaint about not being able to get a listing of all the pages in my domain. This query works:
inurl:shantanuoak.com site:shantanuoak.com
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Many of these special operators are accessible from the Advanced Search page, but some are not. Below is a list of all the special operators Google supports.

cache:
The query [cache:] will show the version of the web page that Google has in its cache.
If you include other words in the query, Google will highlight those words within the cached document. For instance, [cache:www.google.com web] will show the cached content with the word "web" highlighted.

link:
the query [link:www.google.com] doesn't do a normal search but instead finds all web pages that have links to www.google.com.

related:
The query [related:] will list web pages that are "similar" to a specified web page. For instance, [related:www.google.com] will list web pages that are similar to the Google homepage.

info:
The query [info:] will present some information that Google has about that web page.
This functionality is also accessible by typing the web page url directly into a Google search box.

site:
If you include [site:] in your query, Google will restrict the results to those websites in the given domain. For instance, [help site:www.google.com] will find pages about help within www.google.com. [help site:com] will find pages about help within .com urls.

allintitle:
If you start a query with [allintitle:], Google will restrict the results to those with all of the query words in the title. For instance, [allintitle: google search] will return only documents that have both "google" and "search" in the title.

intitle:
If you include [intitle:] in your query, Google will restrict the results to documents containing that word in the title.
For instance, [intitle:google search] will return documents that mention the word "google" in their title, and mention the word "search" anywhere in the document (title or no).