Just the fact that Hanks is the Trope Namer for Tom Hanks Syndrome should be enough, as it truly demonstrated that he really could deliver a powerful performance. But the fact that he won not just one, but *two* Oscars, in back-to-back years - being the only man besides Spencer Tracy to do so, and the sixth man in history to win 2 Best Actor Oscars - to standing ovations each time? That is a crowning moment, right there.
He almost became the first actor to win three Oscars when he was nominated for Cast Away. Alas, this wouldn't be accomplished until Daniel Day-Lewis won in 2013.