I have tried a number of analytics sites/software, and Statcounter is easily my favourite. It updates in real-time and it is perfect for keeping up with what is going on traffic wise with your site from day to day (or minute to minute depending on how much you like to check your stats).
Having a traffic counter that updates in real time can prove to be incredibly useful, because if you find that you are getting a load of traffic to one page in particular from something like Digg or StumbleUpon, you may well want to optimize it for
conversions (more so than you normally would) to get the most from that traffic. If you only use Google Analytics, which updates once a day, you are going to miss out on the opportunity to get the most from the short boost in traffic.
Google Analytics provides a wealth of data, so I run both Statcounter and GA. However, Statcounter pretty much covers everything I would like it to when quickly checking stats for information. I will use GA if I want to check something super-specific. The free version is very good, and I haven't felt the need to upgrade quite yet.
I've also tried Woopra too, and whilst I thought it was very good, I found it to be more of a distraction rather than tool for checking information. So I closed my eyes and uninstalled it. Haven't missed it, so was a wise move on my part.