In a recent promotional email (seen above), Nintendo claims that The Legend of Zelda: Skyward Sword is the deepest Zelda yet.
To me, depth would mean an engrossing story with characters you care about and a game world that feels alive. To others it might mean a lot of items to collect or side quests to embark upon. Dragon Quest IX had a great balance of these qualities and was able to deliver depth no matter what your definition of the term might be.
What does depth in a video game mean to you?