Analytical Tools

Free Analytical Tools, basic functionality is solid, many require you upgrade in order to access advanced features.

• Google Analytics - powerful full featured analytics tool. Has built in feature that gives you accurate financial reporting of ROI by keyword for each AdWords ad position. Google AdWords also has internal split testing and conversion tracking software.
• Google Website Optimizer - almost sure it was release in 2007, it allows you to A/B split test landing pages and track conversion within Google AdWords.
• Microsoft adCenter Analytics - not publicly launched yet, but accepting invite requests.
• Piwik - open source web analytics program
• Site Meter - starts off as free, but charges for advanced features
• Stat Counter - starts off as free, but charges for advanced features and bandwith usage.
• Webalizer - default log analyzer on many servers.
• Analog - default log analyzer on many servers.
• Awstats - another popular default log analyzer on many servers.
  
  
  
  

Cheap Analytical Tools

• Clicky - cheap web based tool similar to Google Analytics. A few less features, but you are not giving all your data to Google either. Also offers a cheap white label analytics package convenient for SEO firms interested in maximizing revenue, and delivering professional unified brand.
• Mint - affordable analytics program that you download onto your computer. One main drawback with Mint is the lack of conversion tracking ability.
  

Affordable Business Analytics Tools

• ClickTracks - Downloadable software and hosted options. Starting at $99 a month.
• Indextools - Starts at $50 a month.
• Weblog Expert - Downloadable log analyzer. Starts at $75.

Expensive / Premium Tools

• Omniture
• WebTrends
• Hubspot - I'm a customer. I use Hubspot to track the performance of my keywords and competitors' keywords (courtesy Gretel Going).
• Website Grader - Hubspot product that will grade your website on a number of analytics and social media indicators. Great free tool!
• Alexa - Some high-level information on website traffic for any site.
• Compete.com - Excellent comparison tool for web analytics-type information.
• Quantcast - Provides good overview of analytics and site demographics (courtesy of Kyra Reed).
• Woopra - Analytics on steroids (courtesy of Kyra Reed).

Background Information on Web Analytics

If you need more background on analytics try the free 44 minute video by Avinash Kaushik.