I don’t think anyone would do an excellent job on SEO without properly using SEO tools (they are free!). Here is a collection of SEO Tools you should be aware of and over time, you should be getting famiar with it and fully utilize it for your site’s optimization.

Code Validation: http://validator.w3.org/
This involves the validation of various HTML or XML standards, which are mainly governed by W3C (World Wide Web Consortium).

Backlink Tool: http://www.webuildpages.com/neat-o/ | http://www.linkvendor.com/seo-tools/site-analysis.html
Backlinks are inbound links that point to a certain website. They are required in order to get good rankings in the search engine results.

Google Sitemap: http://www.xml-sitemaps.com/
Google Sitemap uses a xml format and it is a powerful tool for tracking how’s your site doing in Google

Robots.txt Tool: http://www.123promotion.co.uk/tools/robotstxtgenerator.php | http://www.sxw.org.uk/computing/robots/check.html
Robots.txt is more important than you think. Make sure your site has it and it is in the right format. The first tool helps you generate a robots file while the 2nd checks if your existing one is valid.

Keywords Tools: Keywords Suggestion Tool | Google Keywords Suggestion | Meta Keywords
There are tools that will show you exactly what keywords are popular and give you suggestions based on a core keyword. It also gives you an idea as to what you can rank for and what you can’t. Some keywords are just too popular and therefore too difficult to get a good ranking for.

Keyword Density Analyzer: http://www.seobench.com/keyword-density-analyzer/
Keyword density is important since search engines use this information to determine the theme of your website, the perfect keyword density will help archive higher search engine positions.

Search Engine Ranking Check: Google Ranking | Yahoo Ranking | MSN Ranking
Look how your site rank for certain key phrases across various major search engines.

Website Optimization:
Meta Tag Generator | Spider Simulator | Similar Page Checker | Watchfire WebXACT
These tools in general can help optimize your site. Make sure that everything is up to par for the search engines can take a long time and often requires a lot of experience.