Here at OrcsWeb we've used many different types of site statistics solutions over the years. Each one has pros and cons. The list of cons grows large, and heavily weighted, when the website being tracked generates more than a minimal level of traffic. Very few of the server packages available scale well to handle sites whose traffic is measured in the millions of daily requests like some of the sites we manage.

One challenge we often see is that most programs have a hard time importing log files that grow daily to multiple gigabytes. They have a hard time processing such large files with so much traffic recorded.

Another challenge we often see is that most programs don't handle web farm hosting very well. When there are log files - often still large ones - from multiple sources (server nodes) that have the same date and time stamps, and overlapping IP information, this seems to cause "confusion" and challenges in processing the data.

A solution that is becoming more viable lately is to use a third-party (other than the web host) service to track the analytics. One such option - that we use for our own website - is Google Analytics.

Per the Google Analytics website: 
"Google Analytics is the enterprise-class web analytics solution that gives you rich insights into your website traffic and marketing effectiveness. Powerful, flexible and easy-to-use features now let you see and analyze your traffic data in an entirely new way. With Google Analytics, you're more prepared to write better-targeted ads, strengthen your marketing initiatives and create higher converting websites"

It is very easy to implement, has great reporting options, scales to handle extremely high traffic volumes, and - best of all - it's free! 

Here is a link to additional information about the option with some sample reporting and feature listings:
http://www.google.com/analytics/features.html

Whether your site utilizes Shared Hosting, Dedicated Server Hosting, or Cloud Hosting - this is definitely an option you should consider for your statistical and analytical needs.