If you are after decent web analytics for your site (and if you are serious about your website, you need web analytics!) then the most popular free option by far is Google Analytics, but there is one major issue with adopting google for some web masters.
If you are doing anything that could be viewed as remotely dubious by google, in terms of link building and various ‘grey’ SEO tactics, then as spoon as google clocks the same analytics account on sites that chat alot to each other, they are highly likely to black ball you. If you thenm remove Google Analytics once realising this, its too late, the domain will be tarnished, possibly for good.
To work around this I have recently started using an alternative called ‘Woopra’. Woopra is a killer solution which provides a nice downloadable GUI which works on all operating systems and can centrally monitor traffic on tens, hundreds or even thousands of sites. It is free for every site that has no more than 30,000 monthly pages views, and only starts charging when you’re traffic goes above this. It also has some neat extra features including real time analytics – for example how many people online right now? I still have GA on a few sites, but for free analytics on lowish traffic sites this is the way to go. Check it out!