Google webmaster tools is a must have. Keyword tools are ok. But if you know your niche, and the current trends, you do not need a keyword tool. I have never used a keyword tool on any of my sites.
I usually used SEOpen to check my backlinks, index page, cache and PR for Google, Yahoo, Bing and Alexa. I always do mass checking for all of them.
I use most the google webmasters tool to check my websites, but I'm always looking for new seo tools, maybe get a better idea of optimization. I think is better to see your websites from different viewpoints.
I am always looking for new tools. I had used google webmaster tool, google adwords keyword tool. But right now I am using Seoquake add-on for firefox. Its seems good.
Google Webmaster tool is my favorite SEO tool as it helps me submitting my pages to the site and allows to connect my internal pages to the site, and lots more.