There's something in the way he moves
Completing a game's story and beating the boss is an accomplishment in most games. In the case of Super Mario Galaxy, the game is just getting started by the time you've beat Bowser for the final time and saved Princess Peach and the universe. Miyamoto and team have taken everything they've learned about good and bad gameplay in the last 20 or so years and created a game that's both simple and deep.
Aside from some sadistic RPGs, beating the final boss and being only 25% done with the game is unheard of. In your initial play through with Mario, there's 120 Stars to collect. Doing so unlocks Luigi as a playable character, with whom you can then complete the game a second time. Collecting 120 stars with Luigi opens up the "Grand Finale Galaxy" rewarding the player with two more stars (one for Mario, one for Luigi) and a quick note and picture sent to your Wii Message Board.
Thankfully, getting all 242 Stars (and 9999 Star Bits) is enjoyable to the very last minute. Not everyone may be willing to make that sort of time investment in any type of activity, videogames or otherwise, but you can rest easy knowing that any time you put into this game up until the very end will be something you will not soon forget.
Where Super Mario Galaxy most drastically departs from its immediate predecessor -- the Gamecube's Super Mario Sunshine -- is not so much in what it adds, but what it omits. Gone are the blue coin hunts, water hosing, and kicking fruit from one side of an island to the other. In its place is a purer platforming experience, one where most of your time will be spent running through, jumping across, and otherwise avoiding some of the most creative obstacles to be found in any platformer or action game on any system, current or classic.
Instead of being forced to insert Star objectives into traditional large open-world levels, Super Mario Galaxy's designers had the freedom to create its levels around various play mechanics, many of which have not been seen before in any genre of videogame. It's not fair to spoil these for you, but I guarentee you'll catch yourself giggling to yourself on more than several occasions and wonder why no one has thought of these mechanics before.
There's still some coin collecting in the later stages once the Purple Coin Comet becomes unlocked after beating the final Bowser boss fight. These for some are the one detracter from the overall game's pacing, but for many, especially Luigi's Purple Coin's, these can be equally fun, frustrating, and thoroughly rewarding once you finally earn your Star for completing the level.
The Co-Star mode is great if you have younger members of your family that are not quite ready to grasp the coordination needed to get Mario through the later levels. For the youngest members, they can take control using a second Wii controller and shoot star bits to stun enemies and some platforms in the environments. For the slightly older ones ready to control Mario, you can help them out using the same stun mechanic so they aren't overwhelmed by the enemies. It's a two-sided system that, while useless for the advanced Mario player, is a bright addition that could have easily been overlooked by Miyamoto.
If you have enjoyed any Mario platformer published in the last 23 years or any platformer or action game on any system for that matter, you owe it to yourself and your household to pick up this instant classic.