I agree that extracurricular activities help with demonstrating that a student is well rounded, but I also agree that it doesn't have to be sports. I went to very good school (top of tier two...so not Ivy League, but highly competative

), and I doubt that I got in there because I played sports (poorly) in high school. And in fact, the school claims to not do any sports recruiting, that it is all academic ("and if someone has some athletic ability, all the better"). I find that a little hard to believe considering that they have one of the top tennis teams in the nation, but the rest of the teams are generally mediocre, so perhaps it is true.
And the reason I played sports in high school was to appear "well rounded", and more importantly because it was required of all students to play something (small, private college prep school).