You know, we had 4 kids in my family, with the possibility for more, but after two miscarriages in a row, my mom stopped trying.
I used to know a family that sort of did the quiverfull thing. Last time I saw them, which was several years ago, they already had about 7 kids, and probably a couple more by now. They were religious, but a fair bit more mainstream than the Duggars. The kids wore regular clothes and went to public school, and the older ones weren't forced to take care of the younger ones.
I think having lots of kids is fine (though anything more than 8 is really excessive) is fine, providing you can take care of them, and don't raise them like little robots.
It was mentioned earlier that if the mother had breastfed her kids for a natural, proper length (and believe me, I am all for breastfeeding. I myself was breastfed until 18 months), she would've been pregnant far less often. Breastfeeding is a natural form of birth control, because the body knows that if you're still nursing one baby, you don't need to be having more yet.
The fact is, they're not just letting nature take its course, by deliberately weaning the babies early, they're actively trying to have as many children as possible. This is what I find wrong. I personally believe in birth control and small families, but if someone chooses to forgo it and let what happens happen... that's fine. But I draw the line at deliberately making as many babies as possible and going so far as to alter natural behaviour in order to have more.
The reasons behind this are clear. First, they love the attention. They get money for it. People give them things and they get paid for TV specials. Second, Quiverfull. I've been involved with Evangelicals and the idea that good Christian families should have as many children as possible, in order to "further the Kingdom" and populate the country with good Christian conservatives is very real. I've heard it with my own ears. Hell, there's a billboard for a church in my city showing a couple with a baby and reading "Growing God's Kingdom, one family at a time."
This is not even to mention my disagreements with the way the children are being raised.