I'm VERY convinced that listening to your customers and doing it WELL is a massive competitive advantage.
I've been building an app for the last six months and have been listening to our customers pretty aggressively:
Lots of HN users use Polar so smart crowd.
Part of it has been to build in tools that allow me to manage all the information and to collect as much as possible.
Analytics on everything the user does (but respect their privacy). We're interested in exceptions and things like that...
One our big wins has been to integrate net promoter score and to build out a few tools to analyze the data.
Cohort analysis is also key.
I've been really focused on this and we're gaining about 1% additional retention per week over the last 2 months so this has been great to see it slowly climbing.