dougmc, how old were you when you started biking up hills?
I'm not trying to be smarmy; I'm only asking because, on my first bike (20" kids' bike at 7 years old), I had no choice but to stand and stomp on the pedals. I even weaved back and forth if the street was quiet enough, but there was no such thing as sitting and spinning, even if I wanted to. Standing on the pedals, then, feels natural to me.
What I do today is the same as what I did back then, at least when it comes to standing on climbs: Use a taller gear. It'll have to be tall enough that it feels like walking upstairs or using a Stairmaster at the gym.
The drawback is that, as noted by others, it's harder to sustain. My heart rate spikes when I stand, so my high efforts are only enough for shorter hills. If I can't make it up far enough, I gear down (often just dropping to the smaller chainring in front) and start spinning.