As its own Holiday, under its own name: Rosh HaShanah 4b; Succah 48a
Having its own blessing of Shehechiyanu [Blessing of Special Occasions]: Rosh HaShanah 4b; Succah 47a-48a
It has its own Song in the Temple Service: Rosh HaShanah 4b; Succah 47a, 48a
It has its own Additional Offering, unlike the order of the rest of Succot: Rosh HaShanah 4b; Succah 47a, 48a
How much water is used for the Water Libation in the Temple: Succah 47a, 48b
The bringing of a Bull for the Additional Offering necessitates its own lottery for the Kohanim to partake, instead of joining in the order of the rest of Succot: Rosh HaShanah 4b; Succah 48a, 55b
Which shifts of Kohanim are eligible for the above Lottery: Succah 55b
Its own insertion into the Blessing after Meals: Succah 47a-b
Its own Mitzvah of staying overnight in Jerusalem afterward: Succah 47a, 47b
Its own blessing in the Amidah: Succah 47a-b
Its Torah Reading: Megillah 30b, 31a
Its special reading from the Prophets: Megillah 31a
Special Celebrations
Considering the additional offering of the 8th Day to be representative of the Jewish people, where those of the rest of Succot represented the nations of the World: Succah 55b Mitzvah of Joy on the 8th day of Succot: Succah 48a
Mitzvah of honoring the 8th Day of Succot: Succah 48a
Reciting the Hallel-Prayer of Praise: Succah 48a
Making up Celebratory Holiday Offerings from the rest of the Holiday: Rosh HaShanah 4b; Succah 48a; Chagigah 9a
It has a special Blessing for the King: Rosh HaShanah
4b; Succah 48a
Forbidding Work on the Eighth Day: Chagigah 9a Sleeping in the Succah on the 8th day, and whether this may be a problem of adding to a Mitzvah: Eruvin 96a; Rosh HaShanah 28b