I think it's great. There's nothing wrong or bad or sick about a baby being born. It's an amazing, natural experience - and one that many of us never see until we are having our own babies. And, even then, I can't see what is happening! I've never seen a baby actually be born in real life, unless you consider my four births so far to be ones that I've seen (but my belly was so big and in the way that I couldn't see a thing!).
With my second baby, my 4 year old daughter really wanted to be there. So, we let her. She thought it was amazing. The look on her face when the baby came out and when she got to go over and see him, it was truly amazing to watch. I LOVED it. She is 8 now, and she still talks about it at times. It's exciting to see a baby be born! I'd do it again in a heartbeat.
I am not sure what the cons are in watching a birth, but there are a lot of pros. I say go for it! My sister stayed with my daughter and my hubby was with me. So, we had someone to take her out if needed, but it didn't need to happen.
Oh, and our plan was to have our daughter there when baby #3 arrived, but it happened in the middle of the night, faster than we expected, and she didnt' get to be there in time. Then #4 was a c-section, so she obviously wasn't there! But, I would love to have her there again if I could.
ADDED: I've read some of the other comments and thought I'd add more. I had my daughter watch real births on youtube before the birth. I wanted her to hear what a laboring mom can sound like. And, I wanted her to get an idea of what she was going to see (didn't want it to ALL be so new that she was completely shocked by it all). My sister was with her and talking her through it all and watchful of if she got scared or nervous, which she didn't. She only got excited. At one point things didn't go so good. Baby was 10 lbs 11 oz (and I'm 120 lbs not prego...I'm not a big person), and he ended up getting stuck. It got a little crazy and scary. He was born not breathing and was some blue and had bruises all over from them trying to get him out (poor baby!). It was a relief when he finally did start crying. My daughter was there for the whole thing, BUT my sister was there to take her out if she needed it. She did have to move out of the way for some of it, but quickly things calmed down, and she was able to meet her bruised little brother and immediately bond. There are LOTS of things you can do to prepare her for the experience. And, there's lots of things that can happen during birth and plans might need to change. I personally see no reason to not go for it. It's seriously so amazing to watch your child meet your other child and the excitement on their face.
I don't view birth to be an adult thing. Back in the "olden days" birth wasn't as taboo as it is now. It was a normal part of life and people saw a lot more then as they do now. Children saw siblings being born, and it was normal. It's quite surprising to me the number of people who are anti-letting her watch. I have plenty of friends that have allowed their children to watch, and it's been a great experience for all.
Oh, and you do need to check with your doctor. Our doctor had no issue with it at all, just as long as there was someone to watch our daughter and take care of her.
And, I am someone that likes privacy during birth. I don't want anyone but my hubby and the staff to be there...or one of my children. I don't usually prefer to have my sister there either, but if it's to watch my daughter, then I'm fine with it. But I tend to be very private and don't feel like having my child there interferes with it at all.