My two DDs do it. They love it. Both girls do competitive gymnastics now. DD1 (10) does artistic and trains 18 hours a week, DD2 (7) does rhythmic and trains 6 hours a week.
Pros:
Both DDs started as preschoolers. I have to say that I thought the preschool class was excellent school preparation, as the classes started with a game, and then the coach took the children round a little circuit. The children sat down, the coach showed them what to do, they watched and listened, and then did it themselves. It was great to teach them listening, copying, concentrating skills etc.
Both DDs are very attuned to their bodies. It always amazes me when DD1 says things like she was having trouble with a tumble, but realised she needed to put her shoulder in a slightly different position, and then she could do it. She knows her body so well.
Gymnastics have given the girls a real confidence in life, and ability to cope with anything. Being able to do flicks and free cartwheels etc gives them real streetcred, so when a boy says to DD1 that she's no good at maths, she doesn't care, because she can tumble, and that's much more cool 
.
It has given them a huge circle of friends outside of school. So when there's nastiness in school, and the girls are playing up with each other, it comes to 3pm and my DD just walks away from it all, and into her other circle of friends.
My DDs are incredibly fit and bendy. DD can hold her own in most other sports because she is so fit. And she can give the boys a run for their money with arm wrestling too.
Cons:
It is like a hamster wheel that is impossible to get off. You start with one lesson and they're hooked. Then they join baby squad, and you're they're for an extended lesson a week, then it's twice and before you know it, both girls are hooked, go different days and you're there seven days a week, for up to 4 hours at a time.
It is a dangerous sport. My DD has fractured her bones three times now through doing gym. The better they get the more dangerous it becomes. Just watching my DD do flicks on the high beam is enough to give me mini heart attacks.
It's expensive and time consuming. If they get good, it is a lot of hours and a lot of money.
That said, my DDs get so much out of it, I wouldn't begrudge them it. They're fit, healthy, have very active social lives through the gym, and there's no time for boys, hanging out etc. so I don't mind too much. I've made quite a few good friends through the gym as well now, so that's an added bonus too.