In my opinion Google Analytics is a great service, but it provides almost too much information for me.
I’m using a plugin called Jetpack which uses Google Analytics but automatically filters my own visits to the site out (whenever I’m logged on to my own site that is). It provides all the info you want, such as daily / weekly / monthly unique visitors, what they click, what they’ve searched for to get to your site, etc.
It provides some other nice functionality too, like Akismet integration (that’s for comment spam… or rather AGAINST comment spam), Twitter integration, better spell checker, URL shortener and more by the makers of WordPress in a nice graphical interface.
You can get it free at http://wordpress.org/extend/plugins/jetpack/ – all you need is a WordPress.com API key (which you can get for free, but that’s all explained in the link).
I’m very happy with it.