The statistics are the most interesting webmaster tool for me. They show you how Google is crawling your site, how user queries lead to your site, and what keywords Googlebot is seeing on your pages. For instance, I learned today that I get a lot of clicks for the query pee jokes. I'm #2 on Google for that highly valuable term, although I think #1 would be more appropriate.
The webmaster tools also give you diagnostics for when Googlebot has problems. The Crawl rate shows you how many requests Googlebot is making (3 megabytes a day!) and gives you the option to slow it down. The crawl errors are cool too, particularly for finding robots.txt problems.
The above tools show you what Googlebot is doing; sitemaps lets you help it along. A sitemap is a simple text document that lists all the URLs on your site. Great for dynamic sites with hard-to-crawl pages. This file is understood by all three major search engines, so it's well worth the effort to create one. It's like aliweb all over again!