To be honest, I only really pay close attention to my HR when on recovery rides. I use my HR to be sure I'm not going higher than I should be.
I should be paying more attention during all of my rides. On solo rides I glance down every now and then but try not to focus on the computer too much, on group rides I rarely get a chance to look down since I'm usually just trying to hang on for 3 hours. I'll look over the data after each ride to see whether my HR reflects the amount of suffering I felt on the road.

I could probably be doing a whole lot more with it. I'll probably be reading up on training methods this winter in preparation for the start of my second racing season.