Research is massively important when doing SEO work on a website, whether it is is researching existing status of your site as in how many visitors per month you currently get and where they are coming from, or whether it is researching most popular keywords and keywords which are most competitive.
To be able to get a good understanding of your websites current status these few tools will make your life much easier.
Search Engine Webmaster Tools
https://www.google.com/webmasters/tools/
https://siteexplorer.search.yahoo.com
http://webmaster.live.com/
These webmaster tools tell you lots of different info like indexed pages, inbound links, most popular click though search terms and other info and also has a section where you can submit site-maps of your site.
Stats Programs
http://awstats.sourceforge.net/
http://www.google.com/analytics/indexu.html
Both are very good for checking a whole range of different stats about visitors to your website.