Google Alerts - Get emailed when you or your competitions products are being discussed. Use your company name or domain name along with your competitions, and every time they are discussed online, you will get an email about it. Many times your competition won't realize that people are talking about their products, and you can get in the conversation early and direct people to your website. Also, it is nice to defend yourself if someone is speaking poorly of your business. Another way to use this service is to monitor your high converting keyphrases.
Along with monitoring Google alerts, it is a good idea to do searches on yahoo answers and twitter for your main keyphrases and brand names, and then subscribe to the rss feeds. Make sure to monitor these feeds so you can get in on conversations early. Some times by the team google indexes these sites and you get an update, you are already too late to get involved in the conversation.
Xenu Link Sleuth- Helps you to find broken links on your sites or other webmaster's sites. I use this tool all of the time for finding broken links on my sites, but have you ever thought about using it on other webmaster's sites in order to get backlinks. If you have a site that you would really like to get a backlink from, create an organized report of their broken links, and mail that to them requesting a backlink for your efforts. You may not get a backlink every time, but you are way more likely to get one then just emailing them and asking for one. Also, you may build good relationships with many webmasters in the process. If you would love to have a link from a site - run this tool on their site and send them a nice broken link report. Then ask for a link in return.
Spyfu - This is a great tool to spy on your competition's PPC. Although the data spyfu gets is readily available, they put it in a very nice format to make it easy for you to analyze the data. You can view your competitions adwords campaigns, monitor the organic phrases that they rank for and many other useful tools for competitive research.
Niche Watch - Free tool to figure out why your competition is beating you for a keyword. This tool is simple but very effective. It is not always 100% accurate, but usually it is pretty close.
Traffic Estimate and Alexa - Track traffic on competition or on possible link partner's sites.
If you are thinking about advertising on someone's site, and they tell you they get x amount of hits, notice they don't usually say unique visitors, then check their traffic on these two services. They are not 100% accurate but between the two, you will get a pretty good idea.
Backlink Analyzer - Great tool for analyzing your backlinks. Find out who is linking to you and what anchor text they use. A better but paid version of this tool is SEOelite.
Allinanchor search - Many people don't use this advanced search operator enough. Using all in anchor, you detect backlink networks and other important information about your niche.
Blog Pulse - Is a search engine for blogs. Using this service you can find bloggers in your niche. Once you find them, check their site's traffic and PR. Then you can buy links, oops... I mean request to advertise on their blog. You can also pay them to do reviews on your products or offer to do a guest post. You would be surprised at how helpful many bloggers are to other bloggers and webmasters.
Archive.org - Shows you what pages use to look like. If you are thinking about buying a site, check to see what these sites use to look like. You may find that your friendly health site use to be a porn site... If you are smart you will Block archive.org - from archiving your site. This will be nothing but trouble for you. Many times if you have a legal issue, lawyers will use archive.org in a court case to prove what your site use to say.
SEC Filings and Seeking Alpha - Transcripts and other important documents from larger companies. When researching a new niche you may want to check some of your larger competitions for important documents that might change your direction when creating your marketing strategy.
Ranks.nl - Lots of great tools for SEO. Some of these tools are a little bit dated, but many are still really good.
Optispider - This tool works great for managing your site's page reputation and finding duplicate content/duplicate title tags. The nice thing about it is that it works on MAC, PC, or Linux.
LinkScape This is a tool created by SEOmoz. SEOmoz has many useful tools, but this tool will show you many of the backlinks that yahoo and google wont. Having better backlink data helps you in many ways, but the main thing is that you can easily check your anchor text reputation on a larger scale.
IBusiness Promoter - This is paid desktop software, but I have found it to work very well for analyzing a page's seo. It is not 100% accurate, but it is a very helpful tool for analyzing your site's SEO.
Those are some of my favorite tools, what are your favorite SEO and competitive analysis tools?
Tools Added To List From Other Warriors
Web Tool Hub - Resource of Free SEO and Webmaster Tools ~added by pluto1
What's The Buzz - Tool to monitor Blogs, Technorati, Social Bookmarks and Google Trends for specific keywords ~added by zuluranger
Backlink Watch - Free tool to check details about your backlinks. ~added by ajparker
NicheBot - Paid Keyword research tool to find highly phrases and monitor competition.
~added by ajparker
SEO Elite - Paid tool for doing competitive analysis and many other SEO functions. Similar to Backlink analyzer, but with more functionality. ~added by VladWorks
Google Keyword Tool - Google Adwords keyword tool. Free, easy to use and works very well. Don't forget about this one. ~ added by VladWorks
Micro Niche Finder - Paid software that helps you to uncover niche markets. ~Dan Sherman Marketing