General:
* Event
* Incident
* Happening
* Case
* Instance
* Episode
* Phenomenon
* Matter
* Affair
* Situation
More specific:
* For something unexpected or unusual: Happenstance, chance, fortuity, coincidence
* For something planned or scheduled: Appointment, engagement, meeting, session
* For something frequent or habitual: Custom, practice, routine, habit
* For something significant or noteworthy: Landmark, milestone, highlight, turning point
Other options:
* For a specific time: Date, time, point in time
* For a location: Place, site, spot, location
* For a cause: Reason, motive, trigger, factor
The best synonym to use will depend on the specific context and the nuance you want to convey.