I thought about this a little and it appears that the problem goes deeper than just "should the elf kill the baby hobgoblins?" It actually deals with the entire model of adventuring parties killing all of their foes in any tribal situation.
Assuming all of the providers and caretakers are killed, the adventurers have several options when confronted with helpless hobgoblin (or other) children:
1. Kill them.
2. Leave them alone.
3. Take over from the parents and raise them.
4. Enslave them.
Option 1 is wrong when applied to what SHARK referred to as "moral free agents", good creatures, or any creature whose guilt is not inherent in their nature (this will vary from world to world--in my campaign, orcs fall under the "moral free agent" heading. In SHARK's they don't appear to). If applied to a part of a larger tribe or nation, it could also result in a reputation for the characters as baby-killers and the undying emnity of the children's relatives. Since hobgoblins are lawful evil, the village was probably only a part of a larger tribe or nation so the elf could have hobgoblin bounty hunters on his trail soon.
Other than that, though, option 1 is uncomplicated.
2. Leaving the young alone will probably amount to killing them slowly and cruelly. On the other hand, subSaharan Africa is full of child-headed families and Colin Turnbull described a society where barely weaned children survived without assistance in _The Mountain People_ so some of them might survive if there were older children among them. However, the children would almost certainly remember who killed their parents and left them to fend for themselves. If this didn't amount to killing the children, it would ensure a recurrence of the hobgoblin raids problem in 10 to 15 years. That's certainly not a very good outcome.
3. This is an attractive option for many concepts of "good." It is, however, demanding of time and resources--the characters would probably have to stop adventuring to care for the children. Furthermore, it is unlikely that children from a culture that loves or is attached to their parents would accept their parents' killers as authority figures.
In some cultures, this might be a viable solution if the party were willing to step into the role of an orc or hobgoblin chief ("Your chief was weak so I killed him, now I am your leader--I will teach you how to hunt and how to defend yourselves. Your gods were also weak--they could not defend your tribe from us. We will teach you to sacrifice to gods with Real Power.") Of course, the elvish adventurers might not want to do this or know enough of hobgoblin culture to make it work. It's probably more of an option for a half orc or human.
If hobgoblins are known to be moral free agents, there might be orphanages where they could send the hobgoblin children. However, this is certainly not the case in most fantasy worlds.
In any event, option 3 is only likely to be viable if the defeated culture has a culture which expects leadership of the tribe to be siezed by violence.
4. Selling the hobgoblin children into slavery would almost certainly be profitable although most people would consider it evil.
Historically, this dilemma is the reason that most conquerors did not slaughter their enemies to the last man. If the adventurers had left a few hobgoblin warriors alive, forced them to swear fealty to a king, forbidden them to carry weapons, and forced them to pay an annual tribute like most historical conquerors did, there wouldn't have been any question about what to do with the children.
When dealing with humans, the usual response of historical conquerors has been a combination of 1 and 4 (although I believe that 3 has sometimes been applied between tribes with similar cultures).
The ancient Israelites practiced option 1 when they invaded Canaan (although not after that except in one instance). They were quite thorough about killing everyone. My understanding is that the Hopi Indians also killed every member of one of their villages that converted to Christianity. I think that some medieval conquerors also killed every person within a city which did not surrender but was captured by storm. This was rather unusual though--after all enslaving or subjegating the people was much more profitable. I expect that this option almost never happened unless it was considered to be required to wipe out an impurity (the Israelites and the Hopi) or as a threat to induce others to surrender in the future rather than resisting until the end.
The Assyrians and Babylonians and most conquerors employed a mixture of 1 and 4 when they completely destroyed a city or a people. Those who were too young or old to be good slaves, they killed and the rest they enslaved and divided up as spoils of war.
I can't think of any other practical options and I don't know of any examples of other possibilities from history.
So, if the hobgoblin children aren't moral free agents then option 1 is just fine. If they are moral free agents, then the characters have put themselves into a situation where they have few if any Good options.
BTW: I think ConcreteBhudda's explanation that there are no weak, whimpering hobgoblins (the weak, whimperers were sacrificed immidiately or left to die on a mountainside) is very good if all of the hobgoblin men and women fought to the death rather than attempting to surrender and become leader of the weakened tribe (under the rulership of the party) or fleeing with the young.
