General synonyms:
* Impulsive
* Unplanned
* Unpremeditated
* Unrehearsed
* Unprompted
* Instantaneous
* Immediate
* Natural
* Unforced
* Effortless
More specific synonyms:
* For actions: Impetuous, rash, sudden, abrupt
* For feelings: Unbidden, involuntary, instinctive
* For events: Unexpected, unforeseen, accidental
Examples:
* Instead of "a spontaneous outburst," you could say: an impulsive outburst, an unprompted outburst, an unbidden outburst.
* Instead of "a spontaneous trip," you could say: an unplanned trip, an impromptu trip, an unrehearsed trip.
The best synonym to use will depend on the specific context of your sentence.