Overview: These free and paid tools allow you to track what keywords are sending you traffic, what keywords are profitable, and what keywords lose money. As soon as you start tracking results your campaigns get more efficient because you start focusing on the results.
Tracking where you already rank does not alert you to potential areas of opportunity that you have not yet focused on, but if you track conversions you know what those keywords are worth, and it is easier to rank for keywords related to words you already rank well for than it is to rank for a whole new basket of keywords.
At the bottom of this page is a free video about using web analytics tools.

Free Analytics Tools

These tend to be limited in feature set and give themselves sitewide links on your site, or require you to trust giving a major search engine like Google virtually all your marketing data.
  • Google Analytics - powerful full featured analytics tool. Even allows you to track your ROI by keyword for each AdWords ad position. Google AdWords also has internal split testing and conversion tracking software & offers data integration with Google AdSense that you can't get with any other web analytics tool.
  • Google Website Optimizer - allows you to A/B split test landing pages and track how well Google AdWords traffic converts.
  • Piwik - realtime open source web analytics program
  • Open Web Analytics - similar to Piwik, but more lightweight. Also comes with the ability to record the browser screen on user's sessions.
  • 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.
  • Prosper 202 - free self-hosted analytics tool for affiliates & direct marketers leveraging pay per click advertising. They also have a paid "PRO" self-hosted tier and a monthly hosted subscription service.

Cheap Paid Analytics Tools

  • Clicky - cheap web based tool similar to Google Analytics. A few less features, but you get realtime data and are not giving all your data to Google either. Also offers a cheap white label analytics package convenient for SEO firms looking to add another revenue stream to their businesses.
  • Mint - affordable downloadable analytics program that you set up on your own server. Unlike most other paid analytics programs in Mint does not track conversions.
  • WordTracker's Strategizer - helps bucket data from Google Analytics into groups to help you spot opportunities to grow your organic search footprint
  • Adblock Analytics - see what percent of your visitors are using an ad blocker.

Affordable Business Analytics Tools

  • Weblog Expert - Downloadable log analyzer. Starts at $75.
  • Clicktale - specializes in customer heat maps
  • Crazy Egg - somewhat similar to Clicktale in providing analytics visualization

SEO Update Tracking

General Search Marketshare Stats

Usability Feedback

Expensive / Enterprise Premium Tools

Background Information on Web Analytics

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