Technically, this is a little bit of a cheat: Lily and James Potter died well before the events of the series, but we do see their deaths in flashbacks, and without them, none of the rest of the story would ever even happen. So they're definitely important, and once all the little moments of their murders are pieced together via flashback, they pack one hell of an emotional wallop. James, laying down his life just to give his wife and son a few extra minutes to get away. Lily, given the opportunity to live but instead sacrifices herself to protect her baby. And then poor little Harry, left there in his crib all alone. There's no other way to say it, it's just ridiculously sad.