After reading the comments, I think this can be summed up thus:
- Americans usually do care about their flag.
- Rest of the world, not so much. Some do, some don't.
For me, seeing the Dutch flag wave makes me kind of proud. It probably stands for more than I care to remember, and as my nations symbol.
Most of the time, our flags are used for mourning or celebration. So when I see one, I do tend to stop and think for a bit.
However, I don't feel connected to said piece of cloth. I would question the actions of one who 'disrespects' it. But then again, I don't think that someone else burning a Dutch flag out of spite is disrespectful, just misguided.
For me as a non-American, I find the amount of care Americans take when handling flags baffling. I could never invest that much attention in such an object.
So when you see some people burning the USA flag on TV, the next shot is usually of people angry about their flag being burnt. When there was a protest in the middle east about the Danish Mohammed cartoons, they burnt a Danish flag. And the Danes just shrugged. In my opinion the more healthy attitude.
Then again, most American flags are burnt by the scouts. That just makes me giggle.