Both the best Mario game and the best platformer to date.
When playing the game, I noticed a very similar feel between this and SM 64 in terms of controls. The jumping animations are nearly identical to the earlier game, which I find both convenient and nostalgic. Although the game has abandoned the punch-punch-kick attack scheme, the spin attack works as a fine replacement. The motion controls also work fine; its very unforced unlike some other games (Monkeyball, cough, cough) The highly annoying camera in the old game has also been disposed of and replaced with a convenient fixed camera. Also, the new modes are more diverse, easier to control, and frankly much more fun than wing cap Mario. The galaxy aspect of it makes it much cooler to travel. I've even had fun just playing around with the awesome gravity physics.
Another major strength of Galaxy's is the best visual experience for Wii yet. Not only are the details well done, but the galaxies themselves are colorful and vast. Sound effects are also well done. The game uses very cool music in the background (I'm no music expert).
Its not without flaws, though. The bosses (including the final Bowser) are dissapointingly easy. And while the game attempts coop, to say that it was mediocre would be a huge understatement. The end of the game was also slightly anticlimactic.
In short, for anyone who owns a Wii, this is a must have. This game has raised the bar for platforming to a new level.