I have very strong views on this subject, that I will share. Again, this is my personal view, and since you asked....
I only have my kids in 1 activity at a time. I would never do more than this.
My reasoning, when I was a child, I was ALWAYS doing something. Sports, band, cheerleading (by protest), poms, spelling bees, conferences, FBLA, HRHA, you name it.
As a grown adult, I realized I missed out on just being a kid. I didn't play with my friends in the street, I didn't have a "friendly" game of softball, I didn't hang out on the weekends in front of my house..etc. I missed a lot of my childhood with activities that really didn't give me much as an adult.
I encourage my kids to get into something they want to do. Have done Karate, soccer, basketball, swimming, piano and others. The only one both my sons stuck with and love is swimming. We have swimming lessons and free swim often.
My son wants to go back to karate this year, so we are going to give it a try again. My younger son is happy with swimming, so that is what he is doing.
I have several friends who have nothing but activities for their kids. In 2-4 different sports at once including other activities. It is just too much IMHO. I cannot imagine how running all day everyday from here to there, no matter where you're going or what you're doing, is beneficial to a child.
I find that my children are very independent and self confident when I am around other parents and their kids. The same kids who do tons of activities always seem wired, crabby and just generally not as content as I think my children are. Just my observations and my .02.