I don’t often recommend tools beyond a good text editor. Two tools that I think every webmaster should have on their PC are WebBug, and Xenu. Both are free downloads.
WebBug is a header checker and Xenu checks the links on your site. You can find both at cyberspyder.com and they are free.
I use WebBug to check the header status primarily on redirects. A redirect should return a response of 301 or 302 depending on how the redirect is set up. (I advise against a 302).
Xenue will check your site for broken links.
Both are important for SEO. Here is a tool that I’m currently looking at. It summarizes the keywords by SE that visitors use to find your website. You may or may not find this tool to be valuable. This tool needs to be used in conjunction with other stats programs, but again it is free and worth at least checking out IMHO mylongtail.com.