Hmm - I guess I've been using too high a tire pressure.
Now I'm trying to remember who suggested I use 120 psi - it was so long ago, but it was said with sufficient authority for me not to doubt it. I haven't gotten very many flats in the last 3 years (probably just jinxed myself!), and I am definitely a heavy rider.
So I ust looked up the specs on my wheels and tires: My Mavic Ksyrium wheels (rims, I guess) are rated for 138 psi max according to the Mavic website, and my tires (700x23mm Hutchinson Quartz) are rated 100 to 110, so I guess I am using too much pressure for the tires. Maybe I'll drop down to 100 on my next ride.
Keep calm and carry on...