Moments not mentioned yet and somewhat spoilers this thread encourages but...

The death that Krile in V has to take over.

Beating Trevelyan on Goldeneye.

Fighting Velius in FF Tactics and fighting under Murond Death City.

Beating a strategy building game at a high level like Civilization.

Escaping Midgar under siege and beating Sephiroth.

Personal: The joke the princess tells at the end of Mario 3 that had my brother run down the stairs to tell the whole family.