It may not rank up there with Scarlett O'Hara's declaration never to go hungry again, but Crimson Tide star Denzel Washington says he too once made a vow. While a struggling actor in New York, he swore that if he ever became a star, he'd ''never wash another dish and never take another subway.'' Needless to say, Washington hasn't had dishpan hands or seen the inside of a subway for a very long while. But recently someone got the Oscar-winning actor to eat his words: While on a trip to New York, Washington's son John David, 10, really wanted to see the Big Apple's famous underground. What's a dad to do? Says Washington: ''I walked down the stairs, said, 'There it is,' and we walked back up.''