In most tales, as in Rumpelstiltskin, there is no reason given for fairies or goblins wanting to take human children. I would like to note, though, that in some tales similar to Rumpelstiltskin, the goblin actually wants the girl herself. In the English "Duffy and the Devil" the Devil wants to carry a girl off (presumably to Hell) and in the German "Doubleturk" the goblin wants to marry the girl. (Other Rumpelstiltskin variants are here.)

In a lot of changeling myths, it's suggested that fairies look for beautiful children, perhaps because they want good breeding stock. (See "The changeling of Spornitz.") In these tales they may treat the children as their own and even transform them into beings like them. The Brothers Grimm mentioned nixies who were originally stolen human children ("Nixie Changelings from the Saal River.")

Very frequently, fairies or goblins want human servants, as in "The Daughter of Peter de Cabinam" (from the 13th century) and "The Fairy Dwelling on Selena Moor."

The idea of fairies stealing away humans was very much a danger in European folklore. Fairies found humans to be desirable, whether for labor, or beauty, or another reason. I believe it was a way to explain sudden deaths and illnesses. It was not something to be explained so much as something to be avoided - by protecting pregnant women and newborns, by not angering the fairies, not intruding on their domain (like mushroom circles) and warding them off from your own home by hanging horseshoes over doors or other practices.

If I may put in a shameless plug, here is a list where I tried to collect as many examples as I could: "Why do Fairies Steal People Away?"