If, for whatever reason, you've been waiting for a next-gen sequel to Super Mario USA -- congratulations!
Like Mario's previous Wii and Wii U multiplayer outings, Super Mario 3D World transforms dramatically when you're playing by yourself. But unlike that of the "New" sub-series, 3D World's single-player experience is actually quite good. Levels are designed, not as party-time arenas that bear resemblance to classic Mario scenarios, but instead as tightly-wound platforming gems that you happen to be able to cram other players into.
Everything about 3D World seems better-executed than in the New SMB games. Three-dimensional levels allow much denser obstacle placement; kitty-cat climbing opens up a lot more verticality as well. The world themes cover the traditional bases, but also include space stuff, ala Super Mario Galaxy. Having unique abilities to each character - especially Toad's running, and Peach's floating - benefits the single-player by enabling character-specific obstacles, and the multiplayer by fostering a little asymmetric competition. (The end-of-level score tallies, ala The Legend of Zelda: Four Swords Adventures, also help drive friendly rivalry in multiplayer.) Even the soundtrack is a surprising triumph, adding to the series' lighthearted tunes with orchestral scores and some compelling original compositions. And, of course, the game is graphically stunning -- Nintendo's best-looking production to date.
I can't, in good faith, say that this is Mario's finest adventure; comparing anything to Galaxy 2's platforming perfection still seems unfair. But this is the closest Nintendo's come yet to replicating that success, and the superb multiplayer makes for some delicious icing on the cake.
That being said ... 3D World still holds one last bonus world that I haven't unlocked yet. Maybe there are some even more radical levels hidden away in there. (Incidentally, unlocking bonus worlds and levels is much, much more pleasant than in the New SMB installments.)
Better than: New Super Mario Bros. U
Not as good as: Super Mario Galaxy 2
The world and level etymology is cute, too: for example, "World Bowser-Train" is a level ... on a train, with Bowser.
Progress: 265 green stars, 49 stamps.