The expression, "A healthy soul in a healthy body," is accepted in Judaism. This is true both in the rational stream represented by the Rambam – who feels that it is forbidden to harm the body so that the soul will not be harmed – and by the masters of the Kaballah – who feel that the body is a vessel which holds the soul and which is therefore holy in some way. Thus, guarding over the body and keeping it healthy, in addition to encouraging physical activity, are relevant to Jewish tradition.
However – the root of the culture of sports is Greek culture. This is foreign to the nation of Israel, which always felt that the priority should be the purpose of life – understanding the Creator. Therefore, in spite of the positive elements that it contains, all the excitement around the Olympic Games carries with it a danger of moving away from the true goal of life, the knowledge of G-d.
What is the conclusion? Let the games go on, but we should not go overboard in our enthusiasm.