I am having them, but this is also my first baby, so far it seems that those skipping them are less likely to be on their first baby.
As of now, I'm expecting to have 3. I had a dating one around 7 weeks (I really needed to see the heartbeat, I was very afraid something would go wrong until then due to some prior problems). I am having a nuchal translucency screening tomorrow - if it were just me, I might skip this one, but I'll be 36 and Down's would be a huge issue for my husband, and it's his baby too. [And if we were to have a problem, for the sake of the marriage we'd need to address it sooner rather than later.] Also my practice does a 20 week one. If we found out the gender tomorrow I would consider skipping that one, but again, I'd want my husband's input too (and my dr's, but I'd listen to my husband's opinion more). If there were a problem, I might have slight hesitations about having more done, but I'm sure they'd be overridden by concern for the baby and wanting to make sure everything's ok or do what's best.
If I ended up in a practice that routinely did them at every appointment, as I have heard some do, I would definitely refuse many of them.
I'm not sure how typical I am though - I feel much less "natural"-minded than many of the posters here, but I'm more so than the people I know, and I just felt so much more comfortable with the level of discourse in this DDC than in other forums. Personally I wouldn't make a lot of the decisions others here are making (though health issues preclude some outright), but everyone generally takes such a reasoned approach to things, and remains open-minded, and I love learning about new ideas even if I'm not going to use them (and often a practice that you won't use has at least a little something in it that you will use anyway, I find).