The Legend of Zelda: Majora's Mask is the weirdest game in the Zelda series. It's also the best, even better than its obvious inspiration, Ocarina of Time.
I originally played the game upon its release on the Nintendo 64 in 2000, and I fell in love with its bizarre world and innovative take on the core Zelda formula. It's always been my favorite 3D Zelda game (next to Wind Waker), but I couldn't quite articulate why until I replayed it recently, in its 3DS re-release.
Majora's Mask isn't just great because it's different — though it sticks out even among its odder brethren. Majora's Mask is great because it takes risks that pay off. It comments intelligently on its inspiration, it presents characters and a world that demand attention and even affection and it is the best-realized, best-designed game in the series.