Rosh Hashanah (New Year's Day in September/October) and Yom Kippur (Day of Atonement) are together known as the High Holidays - this makes them arguably the "most important."
The "shalosh regalim" (the Three Festivals) are also very important; they are starting with the Hebrew month of Nissan: Pesach (Passover), Shavuot (Festival of Weeks or Festival of First Fruits) and lastly Sukkot (Festival of Booths). Note that the times of Pesach and Shavuot were adapted by Christians for the celebration of Easter (Latin name = Pascha) and Pentecost (the Greek origin of this name making reference to the fact that Shavuot is seven weeks and a day/fifty days after Pesach).
After the Shalosh Regalim comes Purim, and finally as least important of the ancient holidays is Channukah.
There are also minor holidays like Tu beShvat (New Year's for the trees) as well as fast days peppered all over the Hebrew calendar.