(site:) - Limits a search to a specific domain. In SEO, it's useful to know how many webpages have been indexed under a specific domain, subdomain or directory. Examples: site:www.google.com, site:mit.edu/research/, site:google.com, site:org
(inurl:), (allinurl:) - Shows only those webpages which have the keyword inside their URL. Very useful to analyze competition and keyword density. Example. inurl:tablas, inurl:surf, allinurl:tablas de surf
In the same fashion you can use the following operators for titles and anchor texts: (intitle:), (allintitle:), (inanchor:), (allinanchor:), (intext:).
(ext:), (filetype:) - Limits the search to specific file types, such as HTML, PDF, XLS, DOC and PPT. Example. ext:pdf.
(*) - Any word or phrase. Useful for searches with broad match, but when you still need a specific order of words. Example. food * pets. Will return "food for pets", but not "pets food"
(") - Quotation marks. Use them for specific searches (phrase match). Ex. "food for pets"
(+), (-) - Plus and minus. With + you add mandatory conditions, and with - you remove conditions. For example, food +pets will return all indexed webpages with such words, and food -pets all webpages with word "food" and without word "pet".
(OR) - Combines many possibilities inside a same search. Example. food +cats OR +dogs. This will return webpages with both possibilities.
(info:) - Alerts about possible indexation problems.
(cache:) - Shows the last version of the webpage as stored in Google's cache, and indicates the date and hour it was crawled. Use it to know how frequently Google visits your webpage, and if it's missing some parts.
These are some combinations you can use to evaluate your SEO campaigns:
Competitive analysis: find out who has mentioned you or any of your competitors recently. Example: seomoz -site:seomoz.org during past 24 hours. You can also do similar searches for last days and months For example, d4 means four days, and m4 means four months.
Keyword research: determine the competition over a specific keyword, tracking it's popularity in URLs, titles and anchor texts. For example, inurl:seo inanchor: seo intitle: seo.
SEO auditory: are there problems with canonical URLs? site: citizen.com -inurl:www Do you need to find the strongest webpages for a determined URL inside a website? site: rolex.com +"wrist watch""
Link building: what .org sites do offer opportunities for links with the word "health" in them? site:org salud Do you want to find forums about health? inurl:foro OR inurl:foros salud.