Should I Care About Cadence?

Thanks to the Co-Habitant's love of gadgets, I now have a new cycling computer with an extra feature that measures cadence (the rate at which the cyclist is pedaling). He thought it would be neat to know what mine is, because of my apparently peculiar tendency to not get out of breath while cycling. Even if I am going quite fast (I got my speed up to 20-25mph on flat ground over the course of last summer), my legs get tired, but at no point am I out of breath. For a while, I thought that this was normal and that cycling was inherently an anaerobic activity. But some road cyclists have since told me that if my heart rate is not elevated, then I am "doing it wrong" and need to measure my cadence.

Well, all right. So I have the special computer now and can measure it. I switched to a lower gear and pedaled as fast as I could to see when my heart would start to beat faster. It happened after I reached a cadence of 90 and stayed there for 3.5 minutes. I am out of shape now compared to how I was over the summer, so back then I am sure it was higher. Because I don't like feeling out of breath, my natural rhythm on the trainer is a cadence of around 75-85 - at which point my heart rate is just a tiny bit elevated and I can keep pedaling for quite a long time while absorbed in a movie.

So: normal or unusual? As often happens, attempts to look it up have produced wildly different answers. I have a fairly low resting heart rate (in the 50s bpm), which might also account for why I am not usually out of breath when cycling. But for the most part, I would just like to understand what I should be aiming for in terms of cadence, and whether it is even important to a non-competitive cyclist. For those of you who ride a roadbike: Do you know what your cadence is, and do you care?