Havoc - living close to the school for middle school age sports helped a lot. They had practices and home games for the various sports in different seasons at home (basketball and volleyball) and carpooling was fantastic for sports requiring travel to pitches (soccer) and to away games for b-ball and volleyball. My car seated eight, so I often just dropped off or picked up a large number of kids and their bags of equipment. It was interesting being the fly on the wall/ behind the wheel.
I discouraged soccer all the same, as it was very time-consuming, outdoors in uncertain weather, and half the pitches were a good distance away. There was a lot of carpooling for parties too, especially parties at places like Monkey Island or paintballing venues.
For high school sports, getting them to the school for early morning practices wasn't fun, but carpooling made a big difference. Between them all, they did swimming, water polo, badminton, and football. For home meets, they stayed in school and played whenever the opponents showed up in their busses, and for away meets, they boarded busses and sallied forth. I picked them up whenever they got home (usually 9-10pm), or they got a lift.
I moved closer to the high school when the three youngest were going, and they could walk to and from practices and games.
When they were small, they did swimming lessons in the public pools in summer, and I went to the baby pool with the baby of the day. I also did swim and gym at the YMCA with DCs 1 and 2. Baby DC2 (and DC3 in turn) slept in the carseat poolside while I helped DC1 (and later DC2) in the pool but at age 4 the kids were expected to be in the water by themselves with the teacher and staff. I don't remember doing the YMCA with DCs 4 and 5. Probably too busy.
We did ice skating too - that was a massive pita because lessons were too short to drop off and run, so I spent more time finding a place to park, hoisting small children and babies out of car seats, walking to the rink and getting skates on than the lessons themselves. I have vivid memories of sitting on the cold metal bleachers trying to keep DD3 from killing herself for half an hour while DD2 'learned the snowplough stop' out on the ice, and the horror of realising DD3 was chewing a mouthful of gum she had found stuck to the floor. She had an unerring eye for gum. She was also the one who liked to eat sand.
T-ball was a fun family sport, played on school fields, so younger siblings could amuse themselves on the school playgrounds while the games went on. They all played baseball or softball after T-ball - same fields, same playgrounds, and as the years went by, same families. It was nice to take the folding chairs and spend two hours nattering with teammates' parents. We always started off the season bundled in winter coats and ended up sharing sunscreen.