In Once Upon A Time, the character of Rumpelstiltskin/Mr. Gold seems to have some sort of obsession with kids. In the fairy tale world he made a deal to get Cinderella's first-born. He was willing to even acquire a second baby from her when she lied to him about being pregnant with twins. In the real world, he tracked down Henry, Emma's son, and arranged to give him to The Evil Queen/Regina. Later on he tried to get Ashley Boyd's (Cinderella) child as well. Why's he so obsessed with kids?
As is revealed in Episode 8 - "Desperate Souls":
[Rumpelstiltskin] returns home and uses his power to save his son from the Duke's men. Baelfire [his son] is terrified of this man who no longer seems like his father at all.
It's a fairly safe bet (until the next twist from the writers!) that Rumpelstiltskin's fixation with children comes from the loss (by virtue of fear) of his son when he takes the Dark One's powers.
In a very basic sense, Rumpelstiltskin in the actual stories always asked for the girl's child in return for spinning straw into gold, which her father had foolishly (and publicly) boasted she could do. Put simply, asking for a baby is what Rumpelstiltskin does.
In a philosophical sense, a child, particularly a first child, is a significant and precious 'object' to sacrifice. At the risk of sounding corny, children are the future, they're our hope for immortality.
As a note, in the original story that I recall reading, the girl was going to be killed if she couldn't spin straw into gold, so being asked to give up her firstborn seemed the lesser of two evils.
I honestly figured out that Rumple wants ALL children, period. Why we don't really know yet. But, until all is answered, I think that he simply wants to protect them from the Ogre wars. And EQ. Remember the twelfth episode, Skin Deep? There was a war going on, and the King had to make a deal with him; in this case, the deal was to give Belle to him, for Belle to serve as his maid. Belle is the first born child, even though she is... well, all grown up. But you see my point right?
Rumpelstiltskin the true story.
The Seer in Once Upon A Time said that a child (Henry) would find Rumpelstiltskin son which would make Rumpelstiltskin happy then The Seer says that the child would be his undoing this is why Rumpelstiltskin steals babies he is looking for that child in The Seer's prophesy.
In the show, I’m pretty sure that Rumple kept asking for a child because later in the show, it’s revealed that in his past, he had promised his second born to a healer in exchange for medicine that would cure his first born son from a snake bite. Since Rumple believed he wouldn’t have a second born, he took the deal and went on his way. (This was all before he became the Dark One.)
Although, after he became the Dark One, he returned to the man and killed the healer so that he wouldn’t have to owe him his second born. The thing with him killing the healer, he spent a couple years as the Dark One seeking someone that would deal away their child so that he could pay off the man. That’s why he kept asking for children and asked for Cinderella’s child and Cora’s child. And why he was so eager to accept Cora’s new deal about her owing Rumple his own new child instead of giving him some random kid that she had with someone else.
After years of failure to find another child to deal away, he finally decides just to kill the healer and get the deal invalid.