Google webmaster tools is a great way to submit your site and have statistics from google such as Google crawl errors, the top search queries that your site comes up for and also the top clicks that sent traffic to your site. Google webmaster tools will also show you details on crawl statistics and also if your site is a blog it will show you how many people have subscribed to your sites feed in google reader (Statistics -> Subscriber Stats). Links -> Pages With External Links will show how many pages have links coming into them. Click on the number on the right and detailed statistics will be presented.
Another great Google tool I use is Google Alerts. You can enter search terms you want to be alerted for (or enter your URL) and Google will send out an e-mail based on your preferences. I use this to watch some search terms and also to see when someone links to my site.
These are certainly not the only way to view stats a whole book can be written about Google Analytics alone. What I hope to provide is a couple of new ways for webmasters to keep track of how google views their site and some quick stats.