Depends on the wedding, and the hosts. If the wedding is during the day, outside, and there's plenty of room to run around and it's not going to be a big deal if the kids make noise, and the bride and groom want them there, I think children belong at a wedding.
If the wedding is at night, in a fancy enclosed space, or if the bride and grrom don't want kids there, children don't belong at a wedding.
I have a huge family. When I got married I had so many guests I could barely fit them into the hall. (yes we could have done an outside wedding but fortunatley we did not, it poured the entire day, and night, and next day). Our wedding was an evening wedding, with a reception that ended at midnight. I had my sisters kids be part of the wedding, not the reception. Here's why: The reception started at 7pm, dinner was probably not served until 8:30. Just in my immediate family there were 10 grandkids, most in the 3 years to 6 years old range. Then, count in my cousin's kids, about 15 more. I had to cut it off somewhere, so it was easier to just say no kids.
Thinking back, it would have been a freaking nightmare if all those kids came. They would have been bored stiff, made to "behave and not make noise" in a darkened noisy hall, nowhere to play, pouring rain outside, and past most of them's bedtime.
Some people got their own babysitters, and also my cousin's daughter and my other cousin's daughter (both responsible and well loved by all my nieces and nephews) watched the rest at my mom's house. They slept over and had pizza and movies and stories. The daddies left the reception to put everyone to bed, then came back. My sisters were glad to get out for a night. There were a few people who weren't happy but that's life.
Nobody was nursing and there were no infants, they definatley would have been allowed.
I went to a wedding when ds was 3 months. It was right down the street, luckily, so I left ds with my mom, and drove back twice during the reception to nurse ds. He slept the whole time and we had fun. If it were not that convenient, I would never have gone.
Now that he's 3, I get a babysitter.