This list was compiled by Rav Saadia Gaon:
1. The Shofar is like the trumpet which announces the coronation of a king. That is why it is used on Rosh Hashanah, the birthday of the universe. At that time we accept Hashem’s Rulership. Our tefilos and shofar blasts are like the coronation ceremony in which Klal Yisroel crowns Hashem as Sovereign.
2. The Shofar calls us to examine our deeds and return to Hashem, who will always accept us if we are sincere. This is why we blow the Shofar on Rosh Hashana which is the first of the Aseres Yimei Tshuva.
3. The Shofar reminds us of the Shofar which blew when the Torah was given at Har Sinai; thus we are reminded to study and cherish Hashem’s Word.
4. The Shofar reminds us of the voice of the Nevi’im, whose voices rang out like a Shofar blast in calling the people to do justice and mercy and follow Holy ways.
5. The Shofar sounds like crying, which reminds us of the destruction of the Bais HaMikdash, and thus calls upon us to work for and daven for the Geula.
6. The Shofar, since it is a ram’s horn, reminds us of the binding of Yitzchok, when Hashem provided a ram to be sacrificed instead. Thus we are called upon to be as faithful to Hashem as Avraham, and be inspired by his example of sacrifice and love of Hashem.
7. The Shofar calls us to be humble- its mighty blast reminds us of the mightiness of Hashem and the fact that Hashem is everywhere at all times.
8. On the Day of Judgment, a Shofar will be blown to announce Hashem’s Rulership- our Shofar blasts remind us to prepare for Hashem’s examination of our deeds.
9. The Shofar foreshadows the jubilant return to freedom and peace when we all end up in Yerushalayim in the time of Moshiach- it reminds us to have hope and faith in Hashem’s saving power.
10. The Shofar will be blown in Messianic times to announce the redemption of the whole world, when all nations will recognize that Hashem is One.