What happens to a baby that dies at birth? Do they go to Heaven or Hell, because they never sinned?

Babies that die at birth go to Heaven. Babies that die before they are born go to Heaven too. Even small children who cannot understand the concept of sin and salvation go to Heaven if they die unexpectedly.

There is a point, though, where we do hold individuals accountable for their sins, but that is usually later as they grow older. Hebrew Tradition usually celebrated this age of accountability with a Bar Mitzvah.