This is a topic of Which there is a huge body of work, circulating different theories of why Children are such a prevalent theme of horror, so its unlikely you will find a single comprehensive answer/theory, but there is one unifying reason that all parties are in agreement upon:
Kids are scary, yo.
Children are able to operate as Microcosm for social anxieties. They are largely denied 'a voice' (particularly if they are infants), or when they do have a 'voice' it is distorted by the 'inexperience of youth', and so something that should sound innocent can come across as sinister. Think of "They're here" from Poltergeist, "1 - 2 - Freddy's coming for you, 3 - 4 - Better lock your door.." from Elm Street and "I see Dead People" from The 6th Sense.... but there are plenty more.
As a personal aside (but a good example!) a friend of mine once told me that when he was tucking his son into bed, his 3 yr old son said "Goodbye". He said, "No, its Bedtime now, so we say "Goodnight". His son replied, "I know Dad, but this time its Goodbye"... He slept with the light on that night.
Children are something that are familiar, but still refracted through their own experiences; under-developed and 'alien'. There is no equivalent word in the English language for this apparent dichotomy, but the German word is 'Unheimlich', meaning un-homely (the opposite of what is familiar - or not right within the home, as a place of safety). This is to say the fear doesn't come from something being obviously sinister grotesque, but just slightly not right, but without being able to fully explain why.
German Culture actually has a legacy of being slightly obsessed with the Unheimlich, and Freud wrote a great deal about it (claiming it is where our fear originates). The idea of a Doppelganger originates from the Unheimlich, and as such there are sinister connotations associated with twins. Twin Children, as in the Grady Twins of "The Shining", are perhaps the ultimate representation of Unheimlich.
Children are not governed by the norms of society, as they are not yet participants of it. As our general notions of safety are governed by our shared assumptions to 'play by these rules', and Children are outside of this, they are considered 'Unpredictable', which can create anxiety, often turning them into 'folk devils'.
As an opposing theory to this (Which is particularly pertinent to Horror) Children who have a supernatural or sociopathic understanding of the rules of normality but elect to disregard them are a classic origin of horror.
Damien from the Omen is an example of this type of fear, as he is considered the ultimate 'the Possessed' Child who demonstrates and awareness and is complicit of his own evils. The book You're only Young Twice by theorist Tim Morris features a chapter 'Panic attacks: children as adults, adults as children in the movies' which explores the origin of Horror within these parameters, and will be able to provide you with a long history of terror being extracted from children in this way.
Film Theorist Mary Jackson identifies this films with their own nomenclature as a sub-genre 'Children as Horror', and identifies our fear of these 'Evil Children' as the representation of our societal fear of failing the younger, emergent generations:
‘Not surprisingly, in the run of child-as-monster films, frequently the real point is not the evil of children, often the victims of demonic possession themselves, but rather the ineffectiveness of the family, church, and state – America’s most highly valued institutions – to guard themselves against deception and impending destruction.’
Regan from the Exorcist is a similar case, although hers is a story of the corruption of innocence as penance for her mother's implied heresy/blasphemy/impiousness. Hers is a meta-religious allegory to the Angel of Death taking the children of the impious, but much more sinister: The devil 'takes them', but the terror is not through removal but through defilement.
The most obvious (perhaps) reason for Children being so numerous in Horror needs little explanation:
Children aren't supposed to be scary.
By subverting our expectations of Children as non-threatening entities, Horror is able to force doubt into our natural assumptions, which is a staple of effective horror.
Of course, it's become so common place for Children to be 'Evil' in Horror movies, and this genre tradition has become so entrenched, that its hard not to automatically consider children as the de-facto evil in a horror movie. Such is the way of postmodernism.