The first time I used Web analytics, I mean "really" used Web analytics, was to end an argument. I was running the technical and eCommerce department for an online retailer, a really amazing online gadgets Web site, and the creative director and managing director were near to shedding blood over the following business-critical issue: Should a button on the home page be blue or purple, or maybe it should blue plus purple (blurple), as opposed to purple + blue (purue)? Two hours had gone by, and eight people sat in the room while the two worked themselves further and further away from rational thought and principles of civilized behaviour. I feared for the health, safety and sanity of my work colleagues.
So, I think it's safe to say that I used Web analytics for the first time as an act of sheer desperation. I used to it end the argument once and for all -- I logged in to our new Web analytics software while the two fought, and was able to show them that not only did the customers not care what colour the button was, but in fact, not a single customer had used the button in 6 months.