Thanks to Oyvind I have just installed Mint on my server. This gives me very nice statistics from my site. It runs locally and stores the data in a mySQL database on my server. It works in realtime and shows statistics as people browse your site.
One very nice feature is that Mint supports Peppers. Peppers are plugins made by all kinds of very cool people.
Some good peppers:
Referrer Rollup
Gives you a very nice and tidy list of all your referrers
xxx Strong Mint
Show the IP of your visitors
Sparks!
Sparks! visualizes your visitor data.
Adsense Click Pepper
Get valuable info on how people click on your adsense ads
Foreign Pepper
Show where your visitors are coming from
Feedburner Stats Pepper
Show stats and circulation from your Feedburner RSS-feed
Fresh View Pepper
Fresh View uses XML-based SVG to visualize your Mint visitor data.
Google Images Pepper
Tracks hits from Google Images and let you know about the most popular images on your site. This one is supposed to be replaced by the Referrer Filter pepper, but that one did not work on my first install – so I kept the Google Images pepper.
Trends
Trends analyzes your website’s usage over a set period of time.
eirikso 
I haven’t tried mint myself but google just made parts of their recently aquired Urchin software awailable for free at http://www.google.com/analytics/ . It doesn’t require much of an installation and works perfectly with for blogger.com and similar tools.
[…] StatTraq This plugin will allow you to keep track of every hit on your public WordPress site. It seems like StatTraq gives a very low hit rate because of the wp-cache plugin that I also run. However, I run StatTraq mainly to create the “most popular” lists on my site, and as long as all posts are treated equal this works fine regardless of the fact that StatTraq does not count all visitors. I use Mint to keep track of visitors and referrers. […]