Super Mario Bros.
The original Super Mario Bros. on the Nintendo Entertainment System was an astounding success for Nintendo. Released in 1985 as the pack-in game for the NES console, the game is currently the second highest-selling video game of all time (behind Wii Sports). A simple 2D sidescrolling platformer, you are tasked with rescuing Princess Peach, who has been kidnapped from the evil king of the Koopas, Bowser.
Don't think you have to hunt down an old NES to be able to play this classic. In 2006 the original Super Mario Bros. was released on Nintendo's Virtual Console, meaning that Nintendo Wii owners can easily download and play the game at their own leisure.
Super Mario Sunshine
Released in 2002 on the Nintendo GameCube, Super Mario Sunshine puts the plumber on Delfino Island. While on vacation with Peach and her father, Toadsworth, a villain known as "Shadow Mario"--since it is an all-black version of Mario--leaves graffiti and sludge covering the island. When Mario arrives, he is blamed with the mess and must set out to clean it up using a device called FLUDD, which sprays water around the game world.
The game was generally well received by reviewers and fans bought more than 5 million copies of the game. Because the game was released on the GameCube, it can still be enjoyed on the Nintendo Wii as it is fully backward compatible.
Super Mario Galaxy
Super Mario Galaxy, released in 2007 in Japan and the United States, was the first Mario game designed specifically for the Wii and its motion controller. As per usual in the Mario games, you are tasked with saving Princess Peach from the clutches of Bowser. Unlike other games in the series, this time Mario traverses the galaxy, fighting Bowser's minions.
One of the things that sets SMG apart from other games in the series is its physics engine, which gives each world its own gravity, effecting how the game plays from planet-to-planet.