For me, and most recently, it would be the opening of Dichterliebe by Robert Schumann, sung by Ian Bostridge. And the Andantino from Schubert's Piano Sonata in A major, D 644.
Of course, what triggers the tears may not just be the effect of the music, but the association, or a memory, so Acker Bilk, playing 'Stranger on the Shore' does it most times.
The Londonderry Air, in almost any arrangement is another one, but especially when sung by Johnny Cash or played by Martin Taylor.
There's so much Miles Davis but Flamenco Sketches, or It Never Entered My Mind create some moistness.
And as for Mozart, again, where to begin. Undoubtedly, the Adagio from the Clarinet Concerto. But also, the Finale of Act 2 of The Marriage of Figaro. Interestingly, this isn't particularly slow, which is a characteristic of much 'tearful' music. Then there is 'Tamino, Mine' from 'The Magic Flute'.
Mahler, would include the fifth of the Ruckert Songs, which is heart-breakingly beautiful.
I need to draw the line somewhere lest I spend the whole day listing music, and more importantly I can't find a tissue! It would be good to hear from readers, what music makes you cry?