Antignos of Socho received [the tradition] from Shimon the Righteous. He
used to say: Do not be as servants who serve the Master to receive reward.
Rather, be as servants who serve the Master not to receive reward. And let the
fear of heaven be upon you.
The famous Israel philosopher and theologian Yeshayahu Leibowitz argued in support of Antignus of Socho that the only valid reason for performing the mitzvot is because it is G-d's command. Any other reason, as our mishna suggests, would fall to the status of expecting a reward. No motivation except the fear of heaven, by which we mean acceptance of the commandments, is sufficient reason to compell us to act according to Halacha.
For most of us, it would seem that both Leibowitz and Antignos of Socho are asking of us that we perform the impossible. Even when our motives are pure, our actions are always with an eye of the effect. It is certainly simple enough to eschew the more crass and materialistic rewards that we might think accrue to those who follow G-d's ways. Most of us understand that there is no quid pro quo that attends to those who follow the mitzvot. By the time we have reached adulthood, we no longer think that simply because we are good people that only good things must result.
But putting aside material rewards such as riches or even more spiritual requests such as good health, each of acts with the idea that some good will accrue to us because of our actions. We give tzedakah not because it puts a point on our scoreboard when we stand before G-d, but because doing so gives us the sense of satisfaction that we have done the right thing. We eat according to Jewish law for many reasons: it allows us to participate in the Jewish community; it adds a sense of kedusha (holiness) to the mundane act of eating; it may be healthier. All of these reasons cary with it some sense of reward or compensation for having chosen to follow the laws of Kashrut. In keeping Shabbat we are compensated by the sense of peace and tranquility that setting aside this day brings to us. Indeed, for many with hectic lives, the thought of setting aside a day increases stress, not the opposite and thus they do not observe Shabbat.
Yet, it is possible to understand how we can follow this Mishna if we separate the notion of serving one's master in general from specific deeds that our Master may require of us. The general notion is summed up in the beginning of the Sh'ma when we are told, "You shall love the Lord your G-d with all your heart, with all your soul, and with all your might." The basic thought that should guide us in doing G-d's commands is that we are commanded to love G-d. But the very notion that we can be commanded to love G-d is a paradox. (See Chapter 11 of Louis Jacobs A Jewish Theology for a detailed discussion of this issue). How can we be commanded to love anyone; love is an emotion over which we have no control. Thus, when we truly love, whether it is our parents, our spouse or our children, our family or our friends, we do so without thought of reward. We love and from that love we are motivated to do things that demonstrate our love.
In the same way, if we truly love G-d, then we are motivated to follow G-d's commandments not in the hopes of receiving a reward but because this is how we demonstrate our love for G-d. We run to perform to mitzvot out of our deep feeling of love for G-d. This is how we can be like the servant who serves the Master without thought of reward.