Certainly not considered a conventional instrument by any means, the theremin was conceived by Russian inventor Leon Theremin in 1920.
The feature of theremin that separates it most distinctly from other musical instruments, besides its signature "sci-fi violin" sound, is the way it's played. The theremin requires no physical contact from the performer, instead relying on two metal antennae attached to a wooden body. The antennae sense the relative positioning of the performer's hands, controlling frequencies with one hand and amplitude with the other.
Used in compositions by everyone from Christian Wolff to Jimmy Page, the theremin has achieved an almost cult popularity not only for its method of performance, but for its niche and near-gimmicky usage. Many purists of performance and composition surely would not consider using a wooden box with sonic antennae in any classical or modern compositions - a composer and artist very close to me once called the theremin 'the dumbest instrument of all time'. Nonetheless, its unique nature and incomparable sound certainly leave the theremin in a class all its own.
For more on the science behind the theremin, click here.