With three kids I have a general rule of thumb of 2 activities per child for both practical and financial reasons. DS1 is now 16 and has had his share of activities in the past, I now pay his gym membership and he mainly plays sport at school so he's kind of out of the equation.
DS2 is very dyslexic and finds school a struggle. He has in the past done beavers and swimming lessons but he wanted to stop beavers when his friend stopped going and he's now got to the point with swimming that the only place to go is squads which he doesn't want to do. Tbh if he has any activity on a school night it doesn't really work so he now does an art class on a Saturday morning which he loves. Apart from that though he sings in the school choir and I always let him choose whichever sport he wants at school, even if it involves extra cost. This term he's doing water polo, last term he played tennis. He doesn't ask to do anything else.
DD however is a different kettle of fish. She is 7, has lots of energy and wants to try everything. Previously she has done dance and choir (out of school), but this term she has also picked up swimming and guides. Unlike DS2 she can manage after school activities AND homework. I have lingering guilt though that she is "getting more" than her brother (who is 11 btw). Am I just being silly? What do other people do?