See http://www.google.com/support/webmasters/bin/answer.py?answer=35769#1 for Google's design and content guidelines. And for Google's quality guidelines see http://www.google.com/support/webmasters/bin/answer.py?answer=35769#3.
The search engines themselves will show the popularity of keywords - just by searching for them. Note that the number of results is wildly exaggerated due to large numbers of automatically generated pages that duplicate content to draw eyeballs to their adverts.
Use www.google.com/webmasters to identify keywords, determine who is linking to your site, what people are searching on to find your site and more.
https://adwords.google.com/select/KeywordToolExternal Tells you how many people have searched for keywords and suggests alternatives.
All sorts of free SEO-related tools: http://www.seomoz.org/dp/the-internet-marketing-handbook, http://www.seochat.com/seo-tools/, http://www.submitexpress.com/ and http://tools.seobook.com/.
Where do competitors have back-links: http://www.seosean.com/seo-tools/link-hub-finder/. Enter ten high-quality competitors.
Check Page Rank with www.checkpagerank.net or a browser toolbar plugin.
Check W3C compliance of each page using validator.w3.org.
Online shops should utilise the Google Merchant Centre.
Google Analytics free tools for measuring your site's performance http://www.google.com/analytics/.
Opentracker is similar to Google Analytics but more advanced and is not free http://www.opentracker.net.
For a new site or a site with few back-links, manual submission will speed up indexing:
http://www.bing.com/webmaster/SubmitSitePage.aspx
http://www.google.com/addurl/?continue=/addurl
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