With but one exception, each Jewish holiday has its own specific Mitzvos. Passover has many: eating Matzah, the Seder, and discarding all leavened bread products. Succos has sitting in the Sukkah, Lulav and Esrog. Rosh Hashanah has the blowing of the Shofar, and Yom Kippur, fasting and repentance. And so it goes for all the holidays — with the exception of Shavuos.
Shavuos, which marks the day the Torah was given to the Jewish nation on Mount Sinai, has no particular Mitzvah unique to the holiday. It has Minhagim, customs, like studying Torah through the night, eating dairy, and decorating with flowers, but it has neither Biblical nor Rabbinic Mitzvos. Why is this so?
Torah is a gift from G-d like no other. It encompasses all aspects of Jewish life. From the time a Jew awakes until he retires at night, from birth until his passing, all his actions are guided and circumscribed by the laws and ethics of the Torah. Not just how a person prays, but how he or she conducts business and even spends leisure time, are governed by Torah. When observant Jews travel, they try to ensure they will have Kosher food and places to pray, and plan activities consistent with the laws and ideals of the Torah. It is truly all-encompassing. All of Jewish life is imbued with G-d’s direction, and a Jew must always ask himself, “What does G-d want me to do now?” Of course, there is much room for creativity and ingenuity within the Torah’s boundaries, but the spiritual is always foremost in a Jew’s mind.
Shavuos has no specific Mitzvah to characterize the holiday, because no specific activity could represent an event that so fundamentally envelops all of Jewish life. Thus we spend the holiday celebrating Jewish life itself: studying Torah, praying, and eating festive meals with family and guests. This is both the ideal and only appropriate commemoration for the giving of the Torah at Mount Sinai. (Based on a thought from Rabbi Shlomo Wiener.)
May we all have an enjoyable and meaningful Shavuos holiday, and we may we all appreciate the blessings of living a life led by Torah.