I've used one a lot for bike and run training - pretty much essential tool for most - but only played with it during climbing. The problem with HR is that there's a response lag so that it takes a while for HR to catch up to effort. Even on short, eyeballs out run/bike intervals, the HR won't give particularly meaningful results. It's only over longer, steady efforts that HR comes into its own. So, perhaps for long intervals/routes HR could be useful, but probably not for bouldering or shorter intervals.
One good use is simply for monitoring resting HR - and hence state of fatigue - but don't really need an HRM for that.
Power meters, on the hand, don't suffer these problems. If you can figure out a way to rig up a power meter for climbing, that'd be awesome!