Super Mario Galaxy is one of the most innovative games Nintendo have ever made!
The story of Super Mario Galaxy is that Bowser drags Peach and her up into space by the help of his flying battleships and a giant flying saucer. Mario desperately tries to save her, but is knocked out into space by Kamek. Later, he wakes up on this small planet filled with shiny bunnies. Mario takes his time to play hide and seek with them, and later discovers that the bunnies are actually star children, Lumas. The Lumas show Mario their princess, Rosalina, who tells Mario that she and the Lumas want to help Mario defeat Bowser so they can get back the energy he stole from them, and so that Mario can save Peach. And so their journey begins.
Super Mario Galaxy is a 3D platformer where the objective is to enter a "galaxy", complete a scenario of that galaxy and then get the star, go back to the same galaxy again to complete another scenario to get another star. Once you've collected all the stars you can get in a galaxy, it's time to move on to another one. This is very similar to the gameplay of Super Mario 64 and Super Mario Sunshine. The main objective is to collect enough stars to fuel Rosalina's spaceship so they can travel to Bowser's new intergalactic empire to stop him from destroying the universe.
Each galaxy is different and interesting from one another, and besides the annoying Prankster Comet-missions that block your path until you've completed them or bought them away, the galaxies' missions rarely feel repetitive or dull.
The main game is pretty easy. But that's what makes Super Mario Galaxy fun. It's fair in difficulty, not very hard along the way and only has a few very difficult part here every now and then. But just like 64 and Sunshine, you don't need to complete every mission to complete the story. That's also something that makes the 3D Mario games great: If a part's too hard, you don't need to do it.
The hub-world in Super Mario Galaxy is a giant space ship, which is a very charming and big place to hang out. It's not as big as Peach's Castle from 64 or Delfino Plaza from Sunshine, but I personally like it more than those hubs because it feels more cosy and you feel safe and at home there.
The graphics in Super Mario Galaxy are incredible. They look like they belong on the XBOX 360, for god's sake! Every character model and environment is so colorful and never blocky. The graphics are almost perfect in every way, despite not being on an HD console. The game actually looks a lot better than most 360 and PS3 games I've seen in terms of eye-candy.
The music in Super Mario Galaxy is also very good. A lot of the tracks are orchestrated, which really add to that epic feel that Nintendo were going for with this game.
After completing the story mode, you get lots of things to do afterwards. You can collect all the Green Stars in the game to unlock secret galaxies, you can try to complete every mission in the game, and after you've completed the entire game as Mario, you can do it again as Luigi to unlock the real ending and a bonus picture for your Wii Photo Channel. But overall, Super Mario Galaxy is packed with stuff to do, and even 100 hours into it, you'll still be working on getting all the stars to unlock the real ending.
There aren't any true flaws I have with this game, other than the Prankster Comets, which are annoying because they sometimes can interrupt you on your quest, and they can get frustratingly difficult to complete, especially the later ones. They make unlocking Luigi a pain, and the fact that you have to do it all over again to complete the game at a 100% is just so... URGH!
But overall, Super Mario Galaxy is one of the Wii's best games. It's an absolute blast to play and replay over and over, and the sequel that came out two and a half years later is even better.