If you have any experiences with them, what are your thoughts on them as well?
Piwik - "Piwik is an open source (GPL license) web analytics software. It gives interesting reports on your website visitors, your popular pages, the search engines keywords they used, the language they speak… and so much more."
Unless you're looking for something that analyzes log files, like AWStats. But I'm guessing Piwik is what you're seeking.
How about Google Analytics?
I find it serves my needs, short of giving me ip addresses from visitors. It may be a sellilng platform of the google chart api, but it's very nice to use, I find.
AWStats - "AWStats is a free powerful and featureful tool that generates advanced web, streaming, ftp or mail server statistics, graphically. This log analyzer works as a CGI or from command line and shows you all possible information your log contains, in few graphical web pages. It uses a partial information file to be able to process large log files, often and quickly. It can analyze log files from all major server tools like Apache log files (NCSA combined/XLF/ELF log format or common/CLF log format), WebStar, IIS (W3C log format) and a lot of other web, proxy, wap, streaming servers, mail servers and some ftp servers."
Big Brother Log Analyzer (BBLA) - "Big Brother Log Analyzer, or BBLA for short, is a package comprised of two components: a logger, which logs all accesses to selected web pages, and a log analyzer, which nicely formats the logs into an HTML page. The generated HTML is fully W3C compliant (HTML 4.01/Transitional), which guarantees that it will be rendered the way it should under any compliant browser. Another interesting feature of BBLA is that it is tag-based (you put a tag in each page you want to track): this allows for tracking pages hosted on different servers. For instance, I track accesses to my pages in the School of Information Management and Systems at the University of California, Berkeley, along with these pages hosted on SourceForge in a single file. See the demo for more information."
The Webalizer - "The Webalizer is a fast, free web server log file analysis program. It produces highly detailed, easily configurable usage reports in HTML format, for viewing with a standard web browser. "
Sherlog - "Sherlog analyzes the logs of your website, and sends you a report detailing every visit of the logfile, and summarizing the number of bookmarks, the most important referrers, and the most visited page of the period. Sherlog is customizable : you can choose the numbers of referrers shown, which page to show in the list of most visited pages. Sherlog is released under the GPL : you can use it, copy it freely and even sell it, but you're supposed to let your modifications freely available for everybody. "
Relax - "Relax is a free specialized web server log analysis tool for referrer information processing. It answers the question: "Which search engines, search keywords and referring URLs led visitors to your site?"
I know IIS has some log parsing/analysis side tools which will do what you ask for (Log Parser is one of those tools).
The only thing is this will be responsible for logging/parsing server-side stats, not really SEO statistics. It probably logs stats which can help with SEO, like unique visitors and how long visitors stay on your site etc.
You might also want to check out Open Web Analytics. It too is a PHP/MySQL alternative to Google Analytics.