Read up on stage.scaleMode:
That should be exactly what you need.
Another option to preserve aspect ratio is if you have a parent container that holds everything is scale it to fit yourself:
var widthRatio:Number = stage.stageWidth / BASE_WIDTH;
var heightRatio:Number = stage.stageHeight / BASE_HEIGHT;
if (widthRatio < heightRatio)
{
container.scaleX = container.scaleY = widthRatio;
}
else
{
container.scaleX = container.scaleY = heightRatio;
}
At that point you could either center the container to the stage:
container.x = (stage.stageWidth - container.width) /2;
container.y = (stage.stageHeight - container.height) / 2;
Or do something else with it.