Website SEO Tool | Website Grader this tool grades your site (and gives you a numerical score) based on content and optimization. Each area is broken down into several sub categories, and the analysis also points out what you're doing right and what you're missing or could be doing better.
http://blog.grader.com/ from the makers of the above, but with a focus on blogs (note that my site is a blog and I use both of them as they're complimentary).
Pingdom Tools tests the load speed of your page. Also allows you to save the result online so that every time you use it you can compare the current load time against your previous runs. Also has the ability to run a separate DNS health check as well as trace route functions.
http://services/readability.php#readingresults analyzes the readability of your site using several different algorithms. Aside from the score from each algorithm, you get a break down on how the algorithm works, and an explanation of how to understand the score and how it corresponds to reading level. Ideal for ensuring that you're writing is accessible to a broad audience.
StatCounter Free invisible Web tracker, Hit counter and Web stats Free stat counter that can display number of visits or just track them but hide the results. They have a new beta version I'm testing that goes well beyond what the old version could capture as well, and which tracks more metrics than Analytics (which I believe is essential but shouldn't be the only traffic analyzer one has to rely on): StatCounter - Free Invisible Web Tracker, Hit Counter and Web Stats
SEO Tools | Blogger Sentral checks 6 vital elements of your domain/webpage: it checks your web page size and loading time, page rank, backlinks to your domain/web page, reciprocal links from anyone you may be in a link trade with, broken links on your web page, plus your meta tag content.
I use additional free tools I've found on the web as well, but decided to spotlight these based on the fact that, aside from being free, they're "bread and butter" tools I use regularly, and I'm also particularly fond of them because they combine functionality with ease of access.
Hope they're of help to others, especially other new warriors who really need (and can benefit) from these, and who are already swamped by the learning curve that is part of IM (though I prefer to look at it as a very rewarding challenge).