I'm sure this isn't going to be a particularly acquiescent appearance in the list, but since politics and the opinion of the masses doesn't matter to me one bit I can go ahead and state that Final Fantasy XIII is one of my favourites in the series, possibly even taking the number two slot after XII.
Let's face it: Japanese RPG stories are almost always rubbish, and the characters barely anything more than the thinnest of sketches. Random encounters are an unwelcome relic of the past, and most turn-based combat systems are dull and needlessly lengthy. What keeps you playing them is the stat/gear levelling compulsion. So, make a JRPG with a story so baffling you give up even trying to follow it, but give it a combat system so dynamic, intense and fun it won't even matter.
Oh, and make it staggeringly beautiful to boot.
And by golly is FFXIII beautiful. Frequently on my journey through the game I'd just stand still and gaze around the environments I was in. Environments that only became more impressive as the story moved on. I loved being in this world and because it was so filled with eye candy I didn't even care about the ultra-linear progression, or the slow feed of the whys and wherefores of the tale. To match the visuals it has a superb soundtrack, one that deviates quite significantly from the expected FF norms. Even now just thinking back on some of the sights and sounds of this game I get a warm feeling.
However, what really kept me focused and utterly addicted throughout a 55-hour completion time was that combat system. Sure early on you can get away with hitting X on everything, but a) that's boring, and b) you won't learn anything for later, when pressing X won't get you very far at all. Soon enough you're juggling strategies constantly, micromanaging a particular technique here, whipping out an item there, and the game does not stop to let you ponder a move. Later boss fights are tremendously intense and satisfying, and even lesser encounters are made hugely enjoyable by the stagger/juggle system, which puts the combat more into the mold of a Devil May Cry or Bayonetta. It's no idle addition that you're scored for speed after every fight... employ ill-thought out tactics and you may not only score lowly, you may lose altogether. There's a special satisfaction upon finding the right combination and timing of attacks for a particular enemy, cutting a ten-minute encounter down to thirty seconds.
The next step for Final Fantasy is going to be very interesting indeed, either for its continued push through the boundaries of expectation, or its defeated retreat into tried and trusted norms. Either way, FFXIII stands as a pivotal moment where a genuine chance was taken, and in the most conservative of genres that's merit enough.