Strong emotions:
* Euphoria: A feeling of intense happiness and excitement.
* Rapture: A state of intense pleasure or joy.
* Ecstasy: An overwhelming feeling of great happiness and excitement.
* Bliss: A state of perfect happiness and contentment.
More specific situations:
* Joy: A feeling of great pleasure and happiness.
* Delight: A feeling of great pleasure and enjoyment.
* Exuberance: A feeling of great enthusiasm and excitement.
* Elation: A feeling of great happiness and triumph.
Informal terms:
* Overjoyed: Extremely happy.
* Thrilled: Excited and happy.
* On cloud nine: Extremely happy.
The best synonym will depend on the specific context and the intensity of the happiness you want to describe.