While very little in this world is truly free, the only real cost to using Google Analytics is time, from your PM's, your web admins, your engineers, your email admins, and QA analysts--but it is without a doubt time well spent.
Because you run the risk of paralysis by analysis, one must pick their battles with Google Analytics. If you go in with a clear, concise set of objectives, and a competent technical supporting cast, you will succeed.
On the reverse side of the same coin, if you come in without a purpose, you run the risk of getting bogged down in all of the information without immediate relevance, and you may just leave behind this treasure trove of invaluable analytics in search of said relevance.
For optimizations of anonymous tracking, google analytics is second to none--and it's free! Unless you have extremely high traffic... then it get's very expensive very fast. It is well suited for tracking multiple sales channels, across multiple devices, and allows for very granular tracking. GA supports annotations, providing invaluable context when viewing trends.