In no particular order:
1 - TextAlyser
A simple free lightweight app that takes your url and tells you your keyword density as well as giving link analysis , lexical density and a readability index. Very easy to use, quick and useful! All the things you need.
Another keyword checking tool, one I use a lot! Gives you a run down of your most important words and phrases and their locations on the page, prominence and keyword density. Plus its fast and the site also has lots of other tools which you may find useful such as google positions, links in and out of your site. Put this one to the top of your list. A free-sign up also lets you skip the nasty captchas that are spread throughout to counter bots.
3 - Google PageSpeed Insights
SEO is not only about keyword density and credible backlinks. Your website page speed and efficiency is something that google and a lot of other search engines take a lot of interest in. What good is them putting your website first if it takes 10 seconds to load, people would have left by then.
This useful tool checks your website structure and lets you know where you can improve.
- Minifying your js and css files
- Leveraging browser caching including your images and resources
- Optimising and shrinking the size of your images
- Enabling compression
- Combining smaller images into a single sprite.
Are all things which are quick and easy to fix, you just need to know what they are and how to do it. Pagespeed Insights gives you both bits of information!!
Google WebMaster Tools
Webmaster tools is a great tool for finding out how google is doing indexing your site. Basically this gives you all the information you need to see how your website is coming along.
It shows your most used and important keywords, you can upload a sitemap to google so they can index your site, you can check your rankings across certain keywords and you can see how many times you've been included in search results. All the information is provided in simple bit size chunks and is very easy to keep track of.
Webmaster tools also contains additional tools such as a Structured Data Markup Helper in case you want to add structured data but are not to savvy on how to implement it.
5 - Page Rank Checker
A nice simple site that in one simple step will tell you a websites pagerank! What else could you want?
Facebook and the BBC websites are given a 9 so expect your site to be somewhere in the range of 1-6
6 - Alexa
Alexa is the leading provider of free, global web metrics. Although not for everyone Alexa does provide another view of sites linking your content. And just for that it's worth your time.
W3C Link Checker
8 - Google Analytics
Another entry from google! Google Analytics is a must, giving you details about traffic coming to your site, you can also link analytics with webmaster tools to give you search query data in your analytics window!
You can see how people are using your page, which links they are clicking on, duration on the site and bounce-rate.
All very important information that can help you decide what needs changing on your site
A fremium tool that lets you query one website a week! But that one can give you a lot of good advice!
Giving you a list of top priorities and also information on how to fix them this tool is a great one to start with to see where you are.
10 - Google Adwords Checker
Adword checker is a great tool to use to see if you are missing out on lower priority keywords that you are a part of. Simply enter your website url the category your site/business falls under and a keyword or phrase which you currently use. The checker will then show you how many search results are made every month with the given terms and show you alternatives that might benefit you and raise your rankings!
Also very useful for picking up trends, new words and areas that searchers are looking into.