I went to boarding school and every spare minute of our time when we weren't in school or studying was filled with activities. Mostly sport, which is an old trick at boarding schools for ensuring less of the nighttime high jinks by knackering the kids out. During my time at school I did clubs in tennis, hockey, netball, rounders, cricket, volleyball, badminton, shooting, swimming, athletics, astronomy, drama, fencing, debating, community volunteering - you name it, we did it!
I do remember being absolutely shattered doing my a levels, but it helped me out on my ucas application to have so many extracurricular activities, and I think prepared me really well for uni and the world of work, where I often had to work long hours and burn the candle at both ends.
Personally I'm glad I was kept so busy, as even with all that going on I still managed to find time to experiment with drugs and underage sex, god knows what I would have been getting up to if I'd had more time on my hands! 
I have very young dc now, so not decided yet how I will organise things, but my oldest does ballet, and I'm keen to get her into sport and music if time and budget allow. I think a nice balance between chill out time and structured activities would be good, but I'll have to see how realistic that is to achieve!