Maybe it's a controversial choice, but I'd like to nominate the epic No More Heroes. Regardless of the humor and sarcasm, the storyline was actually brilliant, because it was a fantastic mockery-cum-tribute of various modern cultural phenomena: games, porn, anime, movies, wrestling, superheroes, Star Wars, action movies, fake French accents, lightsabers, cliché storytelling, GTA, racial prejudice, motorcycles, technical superiority - it's as if the game tells a lot more than just what is said and done in it.
Feel free to disagree, but I hope you can follow my reasoning.
Another one on which opinions seem to disagree: Tales of Symphonia. To me, it was just epic, handling issues like the role of religion in society, religious suppression, life and death, genocide, racism - it even had some (unintended?) parallells with the more human side of World War II.
And last but not least, the entire Umbrella story summarized in Resident Evil: The Umbrella Chronicles is nothing special when you just look at the main events. However, it is the eye for detail that makes this series stand out from its peers, with as a pinnacle the genius personality of Albert Wesker. Every event has been worked out from every possible angle to make it all fit: they never needed to, but it does make the series special.
I drink your milkshake.