Formal:
* Festivity
* Commemoration
* Observance
* Jubilee (for a special anniversary)
* Fete (especially for a public event)
Informal:
* Party
* Bash
* Get-together
* Gathering
* Soiree (for a formal social event)
* Hoedown (for a festive gathering with music and dancing)
More specific:
* Festival (a period of celebration)
* Holiday (a day set aside for celebration)
* Ceremony (a formal event)
* Rite (a ritualistic practice)
* Feast (a large meal)
The best synonym will depend on the specific situation and the tone you want to convey.