I've been using Clicky Web Analytics for my blog for about 6 months now and have been very satisfied. It's been a great tool to gather data on the visits to my blog. I'm using the basic free service from them which has many unique features that are not present in other services such as Google Analytics or Feedburner.
It has most of the features expected in an analytic tool and many more. I can see how many people have visited my site, at what time, from what IP address, from which country and city (can also see that on a google map), which browser and Operating System they used, which website they came from, which pages they visited, what actions were performed by them on the blog and how long they stayed on my blog. I can also see how many people have come through search and what search keywords were used.
The display for Clicky website is pretty neat. I can see the referral websites in a descending order in time for any given day. The history of all visits is saved for two weeks as I have a free membership. For paid members, the complete history to the website's use is saved, so one can see what was the pattern on a certain day many months ago.
The free utility service that I am using has a limit of max 3 on the number of websites I can submit for analysis. To get more, one has to get a paid account which is not expensive with a nominal charge per month. For a website with a lot of hits, a paid membership would be useful. The paid account, called premium account has other features like 'spy' which shows live data to the visits to your website in real time.
The website itself is very easy to navigate with good layout and provides most information on my site available with just a click. Another good thing I liked about Clicky was that the script to put into my blog was very simple and small. No other tweaks needed to my blog's source code.
The only downside of using such an analytics for blogs is that one would want to go see the data all the time. It gets almost addictive! Try it out if you haven't already or even if you've been using other analytics tools.