Keyword Difficulty Tool - http://www.seochat.com/seo-tools/keyword-difficulty/
This tool allows you to check how difficult it will be to rank for a certain keyword.
Page Analyzer - http://seogeeks.info/
This tool allows you to check several vital metrics at once.
Keyword Density Analyzer - http://ranks.nl/tools/spider.html
Excellent keyword density tool. This is another Keyword Density Analyzer tool that I like a lot.
Visual PageRank Tool - http://www.iwebtool.com/visual_pagerank
A great way to see the PageRank of all the pages on your website.
Backlink Checker - http://www.backlinkwatch.com/index.php
The most powerful free backlink tool available.
Keyword Competition Check Tool - http://www.justsearching.co.uk/tools/keyword-competition/
You will love this one. Enter the keyword you want to rank for and you can see an analysis of your top 10 competitors.
Robots.txt Generator - http://www.seochat.com/seo-tools/robots-generator/
Use this tool to control what pages you want the search engines to index from your website.
CopyScape - http://www.copyscape.com/
Very useful service that allows you to check and avoid duplicate content.
NameBoy - http://www.nameboy.com/
Having your keywords in the URL of your website is very important. This cool application suggests available domains based on the keywords you want to rank for.
Search Engine Optimization Analysis Tool - http://www.seoworkers.com/tools/analyzer.html
A great way to analyze your pages and improve them for the search engines.
Search Engine Spider Simulator - http://www.webconfs.com/search-engine-spider-simulator.php
This tool shows you a website just like the search engines see it.
Backlink Builder - http://www.webconfs.com/backlink-builder.php
Very useful backlink tool. Enter a keyword and it returns a list of websites where you can list your own site and get valuable backlinks.
Backlink Summary - http://www.webconfs.com/backlink-summary.php
See who is linking to your competitors and ask them for links too.
Google Keyword Tool - https://adwords.google.com/select/KeywordToolExternal
Hands down, the best free keyword tool available. Find related keywords and find out the search volume of several keywords at once.
PageRank Search - http://www.seochat.com/seo-tools/pagerank-search/
Sort search results by PageRank. Very cool.
SEOmoz SEO Tools - http://www.seomoz.org/tools
Probably the best collection of SEO tools in the market. Some of them are paid but most are free.