We welcomed children to our wedding and a number attended, from ages 2-12. They were a delight and not a problem in any way. No one screamed through the ceremony or tipped over the cake. We had a fairly formal wedding at a fairly fancy place.
However, ironically enough, I have since decided that it is probably MORE considerate to hire sitters on-site or recommend/pay for off-site sitters for out of town guests with young children (say, under 5). I can't really support BARRING young children, but making a sitter an option is actually the right thing, I think.
Why do I say this? I just brought my two-year-old to a family wedding. It was very fancy, very formal, at a child-unfriendly place (lots of open fires and candles and grabbable floral displays hither and yon) and involved a lot of people drinking and dancing wildly and a lot of long speeches and toasts. To be perfectly honest, it was VERY stressful to care for my toddler in this environment. They actually did hire a (trusted, family friend) sitter on-site, and although I did not initially intend to use her, we eventually brought DD up to the room where she was and checked in on her a lot. She did fine, till it was past her bedtime (which wasn't long, as it was an evening wedding).
To be really honest, if I had it do over, I think I would have put her with the sitter during the ceremony, brought her to the first bit of the reception so family could enjoy seeing her, then taken her back where we were staying, put her to bed, and paid a sitter to stay with her while DH and I enjoyed the rest of the reception.
I never used to be sympathetic to the "fancy weddings are no place for young kids" argument, but actually, after this experience, I have to say that it may be true that some weddings are not the place for some kids (depending on age, temperament, and the time of the wedding). I have rarely been as exhausted as I was after that wedding weekend! (We also took DD to a fancy rehearsal dinner...)
That said, I totally understand why people feel hurt and upset when their young children are excluded. Some children are also much easier to leave with others--my DD is old enough now to communicate if she needs me, and she isn't one for stranger anxiety. I think the best call is to give parents both options, inform them what the event will be like, and let them decide.