USAA really impressed me recently with a really slick feature: I was in their mobile application, and realized that what I wanted to do was a little too complex for what the app could handle. So I called support, and they (1) automatically identified me based on my number and (2) knew I was just using the app, and asked if I'd like to transfer directly to a person!

It is probably not the most complex integration technically, but it made the experience so smooth.