Analytics
Web analytics means tracking website users and deriving insights or value from those data.
Contents
Local Tools
An excellent program for analytics is AWStats. The nice thing about AWStats, aside from it being free open-source software, is that it's locally installed on your system and so there is no third party. You have your stats, and nobody else does. Another excellent tool for analytics is Piwik. Again, Piwik is hosted on your own infrastructure so nobody else has your data.
wp:Webtrends is a commercial product and is focussed on the SaaS model, but it supposedly is still available as a software product.
Services
Most Analytics systems today are offered as a service. Chief among those is Google Analytics (or GA for short). However, Google isn't the only game in town. An interesting complement or alternative is HubSpot.
In-wiki Analytics
To implement Google Analytics in your wiki, you should not use the googleAnalytics extension or others as they have some shortcomings pointed out by Dantman. Instead, he offers up a better approach: putting the code right in your LocalSettings file.
Analyzing your competitors
A few sites provide insights to any public website.
Enterprise Analytics
There are of course larger analytics platforms or services for enterprise customers. E.g. https://www.ibm.com/analytics/watson-analytics/ from IBM