You want your children to have the best opportunities, perhaps because you missed out on them in your own childhood, or because you want to equip them with maximum talents, or you want to expose them to a variety of activities so that they can find their gifted talent. Is it a good idea to enroll them into as many activities as possible? Or is it best to let them live life at their own pace?
Children get expose to a lot of different activities at school, so a child who is particularly gifted in a general area like music, sport, languages, or mathematics will tend to be spotted. You can then choose to develop this area, or allow them to find extracurricular activities that bring breadth to their lives, not just depth to one area.
I'd be wary of throwing them at everything, just to see whether they're good at it. A better idea would be to pick two or three activities that both you and they would like to go to. Remember that you will also spend a lot of time with the parents at the club, and might even start to get involved with running it. It will be a lot more rewarding if you all enjoy the activity, or are at least willing to help the children practice.
I also think it can be a mistake to push them into things you were good at, or always wanted to do. You should pick extracurricular activities that suit your children's temperament and what you can afford as a family (both in time and money). If your motivation is wrong then your children will pick up and become stressed and anxious about the activity, as they sense that you want something from it that they can't give.
In summary, I think it's a parent's responsibility to give their children access to rewarding and enjoyable activities that develop them as people: physically, socially, and intellectually. That could be extracurricular activities, but it could also be playing with friends in the garden. Pick a few things for your children, but don't get too worried about what they are.
I think it's quality over quantity! I also think kids should trial what they enjoy the best and just pick two or three. School and school work is tiring they need some time out to rest and to play alone.
I think one or two activities per child is enough. Not only does it hurt your hip pocket if you do more, but it is also a stretch of your own time, especially if you have more than one child. Children these days tend to be over-timetabled. They need time for unstructured play and enjoy down time.
I agree, quality reigns. Too many, and your kids will be overwhelmed. I know, as boring as it is for them, time needs to be allocated for some quality family time, as well as for their homework. They need to focus on their school work, both in and outside of school. Aim for 1-2. My nieces did dancing and karate, now they just stick to karate.
I have limited my son to two after school activities. I think a lot of children's schedules get so filled up, they don't have time to be kids. Not to mention parents are often stretched financially and timewise, it can take its toll, not only on the children but the grown ups too. Just like with everything else, moderation is the key.
While extra curricular activities can be fun and enrich kids' lives there is such a thing as overdoing it. There's no point scheduling so many things that your child is exhausted and can't concentrate at school or doesn't get time at home to spend with the family. Also, I think it's really important for kids to have some time to themselves to just BE. Being able to amuse yourself and relax on your own and be happy with your own company are important life skills too.
Extra-curricular activities gives your child the opportunity to meet other children that are not in their class at school. It also expands their skill set, helps brain development, and exposes them to other interests they may not have the opportunity to be part of later in life.
The best solution is to allow you child to choose the activities he/she may be interested in. There will be a greater chance of them staying with that activity for a long period of time.
Make sure they have some time out to meditate, but if you can afford them and the child is keen, go for it! Many gifted children go unextended because they have never been given opportunities. Such children from homes where money is tight should be offered scholarships.
I think it is about balance, and about your child. Too often we fall into the trap of trying to create the childhood for our children that we didn't have. The thing is they have their own personality and interests so it is important to listen to what they want.
Children get tired and can be burnt out just like adults, you are better off doing a few things really well rather than many things poorly.