Looking for SEO testing tool

Try this website. I've used it and it does what you are asking.

Websitegrader

If certainly helped me with a few pointers.

SEOMoz.org is may favorite, they have tons of tools - some free, some you have to pay for. The free tools are plenty for small sites.

Woorank.com is the best one I've come across.

And, a bit off the SEO topic, you should measure the usage of your site with mouseflow.com

I am posting a quick summary of the tools mentioned above, in case it helps others.

Websitegrader - the original tool no longer exists and was replaced by Marketing Grader (pretty useful although no longer SEO focused)

Woorank - I simply love this tool and the free report generated

SEOMoz.org - their Pro subscription product ($100/month) which I tried is fantastic, but what's not clear anywhere is that the rankings only update about once a month, so no need to be glued to stats daily. The schedule for updates is here (I had to email customer service to get this info): https://seomoz.zendesk.com/entries/345964-linkscape-update-schedule Use your free trial wisely (ideally you would sign up right after the refresh and catch another data refresh while still in trial)!

opensiteexplorer.org - this is one of the free tools from SEOMoz.org with some basic SEO checks, focusing on backlinks. There is a limit on free checks so again use wisely.

DIYSEO - I am disappointed with quality of data, entire Link Building section was wrong (as compared to OpenSiteExplorer tool mentioned above). I emailed Customer Service and asked how often it's refreshed. Subscription if only $49/month - half the cost of SEOMoz Pro product so would be a good deal for some if quality of data was comparable.

I will update post with any additional info I discover.

EDIT: Update from a DIYSEO customer service response - DIYSEO uses two different data sets, one for the Report Card and one for the Application itself and the data set for the Report Card is truncated in order to speed the analysis and provide real time responses. So sometimes quick snapshot doesn’t give you the true picture of the site.

SEO Quake and Firebug - addons to Firefox. Free. Easy. Good.

There are already some good answers here, so I thought I'd try to add something different. The W3C provides some great, free tools. While they won't do everything you ask they will help you to see how search engines 'see' your website, and also to ensure your site uses valid markup (important for SEO):

First up is my favourite, the Semantic Data Extractor:

http://www.w3.org/2003/12/semantic-extractor.html

This lets you see how search engines 'see' your website - really useful tool.

Next up is the more well known Markup Validation Service:

http://validator.w3.org/

This will validate your markup, and tell you what needs fixing.

Finally, the CSS Validation Service:

http://jigsaw.w3.org/css-validator/

This does for CSS what the Markup Validation Service does.

There is a new service launched recently that markets itself as a Do It Your Self SEO tool. DIYSEO. They have already been featured in Techcrunch and it looks promising. It is a paid service but on the cheap side if you compare it with what SEO pros charge.