For these examples we will use goasp.net as the website to check. Just replace this with your chosen site and type into Google search:
Listing what is available
info:goasp.net - shows full list of what you can find out.
Page indexes
site:goasp.net - shows the indexed pages of your site.
site:test.goasp.net - shows the indexed pages of your 'test' subdomain.
site:goasp.net/articlecategory - shows the indexed pages of your 'articlecategory' subdirectory.
Page links
link:goasp.net - shows the pages that link to your site.
link:test.goasp.net - shows the pages that link to your 'test' subdomain.
link:goasp.net/articlecategory - shows the pages that link to your 'articlecategory' subdirectory.
Page cache
cache:goasp.net - shows the last indexed version of your homepage. Also will show information about the date the cache was created. Option to view a plain-text version of the page, which lets you see how Googlebot sees the page.
Pages that are similar
related:goasp.net - lets you see similar sites based on your content.