Google Analytics: Free Traffic Monitoring Tool
Google Analytics is an extremely comprehensive, quick-to-setup, easy-to-use, and totally free traffic analytics service from Google. It’s a powerful tool that can help you better understand your traffic/visitors, measure performance of individual pages (or even ad units), identify low performing webpages, and more. (Note: If your website receives less than 50-100 K pageviews/monthly than any simpler analytics tool should be sufficient as well.)

Quick Feature Overview
- Find out where your visitors come from, how long they stay, how many of the come back, what browser / operating system they use, etc.
- Visualize visitors on pie charts, bar graphs and more.
- View visitors by source: search engines (Google, Yahoo, MSN, etc.), website referral, advertising, etc.
- Compare traffic over different time periods (select any date range you want).
- Site Overlay: Excellent features that lets you visualize importance/activity on every link on your website/blog. (no download required).
- Conversion Tracking: Measure the effectiveness of your advertising campaigns and identify top performing webpages.
- Complete integration with Google Adwords.
- Schedule personalized email reports.
- Multi-Lingual: available in English, French, Italian, German, Spanish, Dutch, Japanese, Korean, Simplified Chinese, Traditional Chinese, Portuguese, Danish, Finnish, Norwegian, Swedish, and Russian
- and lots more …
Google Analytics: Introduction
Google Analytics - Context and Actionability
Check out Google Analytics @ [www.google.com/analytics/]

What about the alternatives?
You can try W3Counter.