HTML improvements – The report shows how well your site does behind the scenes. Information like if you have missing, improper or duplicate title tags, descriptions and even content are definitely items you’ll want a heads-up on. HTML Improvements will help you do exactly that, make improvements!
Search Queries – The single most useful report by far, Search Queries returns a wealth of data including impressions, clicks, click-thru-rate, keyword terms searched, image and video SEO and more. The keyword section only goes back for 30 days, but it gives you some data you can plug into other tools.
Crawl errors – The Crawl Errors report will show you which of your pages aren’t resolving to their requested URL. This typically shows up in the form of a 404 Page not found error. It’s very useful to have this information, as it may be a simple matter of fixing a URL, link or redirecting.
Links to your site – This one returns a list of sites that are linking to your pages, and will show you what pages are drawing the most interest. This can be, and often is, quite surprising, as pages or content you might not have thought was significant may very well be drawing loads of traffic to your site!
Google Webmaster tools are a very useful tool to let you know what you need to be concerned with and fixing within your SEO. It ought to be your first stop, even though you may eventually use a more sophisticated paid tool to dig deeper.