Paper Mario: The Thousand-Year is, without a doubt, one of Mario's best outings. It improved on everything from the original Paper Mario and made them better.
The story is, indeed, the best you'll find ANY Mario game. Period. It starts out as a standard hunt for Princess Peach, but as you get further into the game, the story becomes interesting and dark. I'm not going to spoil anything for you, but let's just say that you'll be shocked at how dark the story gets near the end of the game.
There are eight total chapters in this game, and each chapter has a subplot. If the main storyline isn't enough to draw you in, then maybe the subplots will. Each chapter has its own quirky subplot, and they can actually be fun and interesting to follow. You'll be going to all sorts of places in each chapter. These places generally have towns that are fun to explore and well-designed dungeons that are fun to explore as well.
The graphics have a fun, distinct style. All of the visuals are consistent with the paper theme, and they are very pleasing to the eye. The graphics look even more papery than they did in the predecessor. In the first Paper Mario, the graphics had more focus put on detail than they did paper, but The Thousand-Year Door ditches detail for paper effects, which in turn gives the game a unique visual style that never makes the graphics look dated.
The soundtrack is also a nice part of the game. It's not as good, or memorable, as the soundtrack of its predecessor, but it's still good nonetheless. Each song strikes a perfect a mood for the places and cutscenes, and it's overall very well-done.
Gameplay wise, this is anything but your average RPG. Sure you standard RPG-related things such as going through towns, collecting information, fighting enemies, exploring dungeons, solving puzzles, and fighting bosses. The combat system is some of the best you'll find in the genre. When you encounter an enemy, you'll go on a fighting stage where you are viewed by a large audience of familiar faces (e.g. goombas, koopas, and many others).
The combat is turn-based, and the attacks are executed by timed-commands. The timed-commands and audiences are what keep the combat fun throughout the game. New allies, special attacks, and enemies are introduced through the course of the adventure, and they shake things up and prevent tedium from settling in. You can also block (A button) and reflect (B button) damage during an enemy's turn, which is a great feature that the first Paper Mario didn't have.
Just like a lot of RPGs, characters play a large role in this game. You get one new ally in almost every chapter. Each character has a fun personality, and each of them is likable. The allies are now given HP, which is a great feature because you can have your allies take damage for you during combat.
Paper Mario: The Thousand-Year Door, and its predecessor for that matter, does away with a lot of the complications that most RPGs have. Leveling up is made simpler, and it's easy to understand. You also don't have to do a bunch of grinding in order to perform more powerful attacks because more power is added to the attacks when you acquire a new hammer and boots. You can level up HP, FP (Flower Points, which are used to perform certain attacks, and BP (Badge Points, which can be equipped to Mario and his allies in order to perform various things that occasionally use FP). Leveling up is done by earning 100 star points, which are obtained by defeating enemies.
You've probably noticed that I've given this game a lot of praise and haven't discussed the downsides, so now I think it's time that I do so. One of my biggest complaints about this game is that even though the difficulty is very well-balanced, the final boss battle is ridiculously hard. Another complaint I have is that some of the enemies can be annoying to fight, such as the ones that generate shields around them, the fuzzies, etc. You also can't skip any cutscenes, which can be very annoying if you die during a boss fight and have to watch the cutscenes all over again before retrying the battle. These are minor complaints, but they are worth pointing out.
Overall, Paper Mario: The Thousand-Year Door is an amazing game. It has an interesting story, a great visual style, fun combat, and a very well-balanced difficulty level. If you have a GameCube or Wii, then you simply must give this a try.