In general, the music has a calypso feel that reminds me of the original Super Mario Bros game. And many of the NSMB Wii themes, like the Underwater Theme or the Beach Theme, while not a direct remake of the original, call to mind classic themes like the Super Mario Bros Underwater Theme or Super Mario Kart's Koopa Beach Theme. Likewise, for a thirty year old gamer who can remember playing the original game, some of my favorite moments in the game music are those tracks that bring back classic themes from previous games. Many of the sound effects, the death sound and the "Help me!" cries of your character-- which actually play from the Wii remote speaker (Wiimote as I call it). These bring a cool added dimension of 3D spacial sound for the player that highlights the audio advantage the Wii has by giving you a speaker in your hand. There are other touches too: the layering effect of adding percussion (first used in Super Mario World) when you get on Yoshi in NSMB Wii is still a part of the classic audio experience.
Several of the short, classic themes make a reappearance, for instance, The P-Switch, Star Theme, Course Clear (with fireworks), and Princess Peach Rescue Theme come to mind immediately. However, some longer themes make an appearance as well as remade, updated versions. These are some of my favorite sound tracks in the game because they bring up nostalgia from my childhood, particularly from Super Mario Bros 3, which many gamers of my generation would consider to be the "best" of the Super Mario Bros classic games. For instance, the Koopa battle theme is a remake of the theme from Super Mario Bros 3. Compare:
The Hammer Bros Theme from SMB 3 is redone as well for this game for the battles that occur from encounters on the world map.
The Underground Theme from the Original Super Mario Bros also gets a remake in this game. I never thought about the original not being in common time, but as I re-listen I realize that it got moved to 4/4 at some point. These first examples have all been lengthened in some way from their original versions.
My favorite classic remake, though, is the airship level theme. Not only was I super pumped to see an airship level because they are so much fun, when the music starts up, it's an absolute flashback to my childhood. This is the first remade theme I've listed here that's not in the same key as the original.
Other miscellaneous audio thoughts:
While not a direct remake, the Volcano Level theme reminds me of Ganon's Dungeon Theme from the original Legend of Zelda. The World Map 3 theme, being an icy world, uses sleigh bells in the instrumentation to convey that sense of holiday/winter that is prevalent, at least in America. Similarly, the Snow Level theme is the same as the new Overworld theme of the game, but has sleigh bells playing in the background. It's a cool way to make the music sound wintery (Christmas-y?). Compare Leroy Anderson's Sleigh Ride. The Giant Bowser theme incorporates organ and chimes, classic sounds that invoke the ideas of death and godlike imagery common to many games, but of course, I think of Final Fantasy IV Golbez theme and Final Fantasy VII, Sephiroth's theme.