It is an unfortunate and rather ironic fact that what are generally considered to be Mozart's two greatest choral works- the C-minor Mass and the Requiem- were both left unfinished. In fact, with Mozart's reputation for being one who wrote quickly and with little effort, we in the choral world might complain of unfair treatment. After all, our opera neighbors don't have to put up with stuff like this. Imagine if the man had just decided to stop composing with Pamina and Tamino wandering around in the fire and water-what kind of ending would that have been?
With the Requiem, we have to grant that Mozart had a pretty good excuse for not finishing (he died). Anyway, since there was money riding on its getting done, his wife went out and found somebody else to get the work across the finish line, meaning that while it isn't all Mozart, we at least have a complete piece. We are less fortunate with the C-minor Mass (there was no money hinging on its completion), and more justified in feeling slighted that Mozart never got around to finishing it.
While Mozart's earlier Mass settings for Salzburg had been brief works with through-composed movements (the Archbishop apparently didn't go for long services), in the C-minor Mass he divided the longer tests into several distinct movements, alternating extended choirs (up to five and eight voices) with melodious and/or virtuosic solos and ensembles to create a cantata-like form reminiscent of Bach's B-minor Mass. As for inspiration, it seems that Mozart had sworn- be it to God, himself, his father, or someone else- to compose a Thanksgiving Mass if dear old dad would forgive him for marrying Constanze (Leopold apparently wasn't a big Constanze fan). In any event, he began work on the project in the fall and winter of 1782, and by early 1783 he had set the complete texts of the Kyrie and Gloria, as well as the first two parts of the Credo. Mozart was more or less obligated to perform the Mass during his visit to Salzburg in the summer and early autumn of 1783, and even though he put it off until his last day in town (I'm not making this up), he still only managed to add the Sanctus and Benedictus. Although he had only an incomplete Credo and no Agnus Dei whatsoever, Mozart kept his word and put the thing on just the same. Just how he got around this during the performance we still don't really know, but whatever happened, this was the work's first and only performance during his lifetime (Constanze sang all the big soprano solos to show Leopold that he was wrong about her). After that, Mozart put the score away and never worked on it again.
He did, however, steal some big chunks of the Mass in 1785 for a now-obscure Italian cantata 'Davide penitente', and it was in this form that the music of the C-minor Mass became popular in the nineteenth century. Its genesis as a Mass composition was forgotten until the early years of the twentieth century. At that point, in looking at the sources someone realized that although both the Sanctus and the Hosanna in excelsis had been written down as four-part choral settings, their musical substance implied a double-choir and double-fugue, respectively. (Just why Mozart might have wanted one thing and wrote down another is kind of complicated- let's just take the musicologist's word on this.) Anyway, the manuscript has been lost since WWII, so these particular movements were "reconstructed" by H.C. Robbins Landon between 1953 and 1955, making them "intellectual property". To summarize, it's all Mozart's fault.