What are the most popular data science application use cases for consumer web companies
Satisfaction is a huge one that I run into a lot.  Huge referring to importance/difficulty/complexity.

The bottom line is that for very large services (search engines, facebook, linkedin, etc...) your users are simply a collection of log lines.  You have little ability to solicit feed back from them (not a hard and fast rule necessarily).  So you have to infer their positive or negative feedback most of the time.

This means finding ways, even outside of predictive modelling, to truly tell, from a collection of log lines, whether or not someone actually liked something they experienced.  This simple act is even more fundamental (in my biased opinion) than a/b testing since you're talking about metrics you will eventually track on a test scorecard.

Once you have a handle on good SAT metrics then you can start making predictive models and experimenting.  But even deciding what piece of log instrumentation can tell you about SAT is non-trivial (and often changes).