Final Fantasy XIII
I'm surprised that nobody on this board is talking about this game. It's been filling every spare moment of time I've had over the past two weeks. I've put in nearly 70 hours now, and I'm still at least 10 - 15 away from getting the platinum trophy.
This game is a departure from the Final Fantasy norm. The changes have turned some people off from liking the game. But, as with a great many things in life, this game needs to be given time to fully understand why the changes were made and how they ultimately turn out.
Instead of the story being slowly and gently introduced while the battle and level up systems are thrown at you all up front, this one is the opposite; you'll find yourself thrust into the middle of a fast-moving story and the battle system starts out extremely basic and slowly expands as you play.
As you play you'll notice that you're not leveling up or gaining gil (money). You also don't have a clue what's going on, other than the fact that your characters seem to be caught in the middle of some kind of war. The characters use plenty of jargon, leaving you scratching your head rather than understanding. But don't worry, it's supposed to be this way.
Before long, some major events happen in the story and now your characters can level up and gain new abilities. This expands on the combat a bit. However, a little further into the same chapter you will be shown how to use this game's class/job system. At first it seems kind of trivial, but before long you begin to learn how integral it is. The battles are fast and frantic, and the strategies required for this class system become complex very quickly. It ends up being very interesting, especially with the level of complexity available in the latter half of the game.
After playing over 70 hours worth of this new battle system, I can safely say that I love it. It's not quite perfect, but if they build on this idea for future games, I think they'll have a real winner. I haven't been this impressed by an RPG battle system since Grandia II. Though that one is still the best, IMO. 
When it comes to liking FFXIII, one of the biggest hurdles for modern gamers to get over is the linearity of this game. Yes, it's extremely linear from start to finish. Most zones have very few branches along the path and you typically cannot return to a zone once you've moved on to the next one. The story will frequently flip you between groups of characters as they split up and meet back up throughout the story. The story moves you along, rather than you moving the story along. But it is this trait which allows it to keep the perfect pace.
So can you handle linearity? I don't have any problem with it. Linearity is necessary for the best and most epic storylines. Movies and books are 100% linear, and RPGs are basically an interactive version of those other storytelling mediums. This isn't a Choose Your Own Adventure book. Instead, this is you along for the ride. You're brought closer to these characters as you go through their trials and tribulations alongside them. It's like a great novel or movie, but you get to be right there in the thick of things as the plot unfolds around you. The best storytelling can only be done through linearity. This game just wouldn't have worked any other way.
Put it all together and you have a fantastic game. I would liken FFXIII very much to Final Fantasy X, which was one of my favorites of the series. FFX was also quite linear, but most people don't seem to remember it that way. FFXIII shares many similarities, from it's rather linear but very interesting story to it's very real character personalities to it's leveling system. The 'Crystarium' leveling system in FFXIII is basically just a 3D version of FFX's 'Sphere Grid' leveling system.
Ultimately, I highly recommend FFXIII to fans of the series. It may take some time to get used to the changes, but you'll begin to find that the game introduces the various facets of the battle system to you at an excellent pace. It would just be far too much to get it all up front. So don't go in with any expectations and just let the game win you over by itself. If you hear anyone complaining about how they don't like FFXIII, they probably just didn't play far enough into the game to see what it's really all about. 
If anybody on this board has any questions about anything in the game, I'd be happy to help. I've been pouring over the 200+ page strategy guide and scouring message boards to learn all I can about the various systems in this game. Whether it's the battle/Paradigm system, the upgrade/dismantle system, the side missions, Titan's Trials or just CP or gil farming, I've got a firm grasp on pretty much all of it. I only have a few missions left (I 5-starred most of them) and I'm working on mastering everyone's fifth role/class. I've already beaten some of the toughest battles in the entire game, but I'm not stopping until I've done it all. Platinum trophy, here I come!
By the way – if you have the choice, go for the PS3 version over the 360 version. I have both and it's a massive difference.
The thing I don't like about this game's storytelling is that it pretty much forces you to look into the in-game database to understand what the hell is going on. Instead of explaining some of the terms in the story, the characters spout off all this nonsense and act like everyone (including the player) knows what they're talking about. Sure, other things like the original Star Wars kind of started off like this, but at least they explained themselves eventually, whereas FFXIII doesn't really explain much of anything at all unless you read the database. And let's face it, when the devs make you read a database to get the story, you know there's a problem with the storytelling.
Plus I think its stupid how the Fal'cie force the l'Cie to figure out their Focuses for themselves. If the Focuses are things the Fal'cie want done, why do they not just tell the l'Cie the Focus so that they know what they're doing and can complete the Fal'cie's mission (thereby giving the Fal'cie what it wants, instead of allowing the possibility for failure)? I realize they're supposed to be mysterious, but the Fal'cie appear to be giving up common sense for their mysterious nature IMO.
Oh, and the weird Japanese stuff (like a Chocobo living in Sazh's hair, the gunblade, etc.) made the story lose any tone of seriousness it could have had. I realize its a JRPG and its Final Fantasy, but even in a game like this at least a few things should make sense.
I will give the game credit for its characters, though; they're likeable and one of the only redeemable qualities of the game's story (excluding Vanille and her damned Australian/British/American accent).
Also, the gameplay's pretty good, and its one of the most enjoyable aspects of the game IMO. However, with such a bad story (IMO) and with this being a story-driven game, the gameplay didn't make up for the stupidity of the plot, the weird Japanese stuff, and Vanille.
So overall I'd say that it was a decent week-long rental, and I would only recommend this game as a rental to a normal gamer. However, to all the FF fans out there, I'd say buy it since the linearity of the game doesn't really take away from it (as Asaic pointed out) and the style is still distinctively FF.
And also like Asaic pointed out, the PS3 version is highly superior to the 360 version, so if you really want to buy the game I would suggest that version.
Wow, you have some pretty strong feelings about the game. 
It seems to have made an impression on you, even if you didn't like it much.
I completely disagree about the storytelling method with the Datalog aspect. This game uses a lot of jargon that is common terminology to the locals. It would be pretty silly if they had to stop and spell everything out every time because they would be totally breaking the fourth wall. It would be really cheesy and would slow down the story and the pacing.
Furthermore, you don't need to read the Datalog. It can fill things in if you're the type of person who, like me, enjoys knowing every detail. But it's far from necessary. You can learn enough to understand the story without it. I know several people who never bothered to read the Datalog at all and they feel that they understood enough by the time it was important to know about it.
Your Star Wars analogy is pretty accurate. When I went through FFXIII the second time, I had a completely different perspective and I caught things I didn't the first time. Nothing important, but definitely interesting. I like that. It's like a replayability factor for the story.
I know that Vanille is quite unpopular, but I like her. The voice acting is cute and suits the character. The voice actress is Australian, so it's not a fake accent. The character has a great visual design IMO and she was the most complex character in the game. The entire story sort of revolved around her.
While the plot in FFXIII is unusual, I think that's one of its biggest strengths. People tend to pigeon-hole Final Fantasy games' plotlines, but they actually do have a fair amount of variety in the details. FFXIII is one of the most unique in that regard. It's not the most interesting Final Fantasy universe, but it is far from the worst, IMO. FFXII's world and plot felt much more bland to me.
This game also features a lot of Japanese cultural influence. When they write Final Fantasy games, they don't write them for an international audience, they just write what they know. Japanese storytelling is fairly different from western storytelling. Personally, I'm a huge fan. I grew up with a lot of Japanese influence and I even lived in Japan for a while as an adult. I totally love the culture. This enabled me to fully enjoy the nuances of FFXIII. Regrettably, FFXIII leans very much towards Japanese cultural idiosyncrasies and that can alienate some players. While it doesn't bother me (I rather enjoy it), I can totally understand it turning players off. I couldn't help but have this thought in the back of my head as I played through this game. Oh well.
That is the reason behind the mystery of the Fal'Cie, by the way. It's a Japanese thing. They like the concept of god-like things being very mysterious and never fully explained. It mirrors many real-life religions. If a god wants you to do something, they don't just give you a written page of instructions, they give you visions and other vague impressions to point you in the right direction without actually telling you anything. It would be kind of boring if you knew exactly what to do and could then decide to just quit and go home, rather than stumbling upon a greater truth and having to make a crucial decision at a key moment. I like it the way it is.