Robert Schumann's Traumerai is one of classical music's best-known melodies. The original work is for solo piano, and many piano students learn it (though, to my recollection, this one never came to me during my years of piano instruction). There's a wonderful book by NPR's Noah Adams, Piano Lessons: Music, Love, and True Adventures, in which Adams chronicles his year of piano lessons at the age of 52 when he wants to learn Traumerai so he can play it for his wife.
Even though the piece is best known and loved as a piano work, it has--like all the great classical works--been ported to other instruments and ensembles. This one, I find especially appealing: it's for solo cello with piano accompaniment. I hope Schumann would approve.