Useful online book on statistics. A work in progress, but looks very valuable.
Web action analytics. Tracks events rather than pageviews, so users clicking "Like", etc. All data in real time, detailed analysis, retained >3yrs. Pricing is free up to 25k data points, $150 for 500k, and upwards. Interesting.
QuantCast stats on the WordPress.com hosted network
Woopra is a free web analytics tool with a focus on real time analytics. Track visitors live, even talk to them in real time.
Crazy Egg adds a new dimension to analytics. It includes a heatmap where you can see where users are clicking on the screen, and other visual presentation tools. From $10 for 10 pages (10k pageviews), up to $100 for 100 pages (100k pageviews).
Mint is a self hosted web stats package, commercial, about $30 per domain (I think) as at May 2008.
Web Analytics system similar to Google Analytics that supports live "spy" view that shows page views as they happen.
Use WordPress.com's stat service on your standalone WordPress blog.
An open source web analytics framework with in-built integration for WordPress and MediaWiki.