First of all, if the players aren’t personally invested in the story, they won’t care about its outcomes. This mini-essay will give you a lot of food for thought, handy tips, and advice for how to foster personal investment in the game and, more importantly, how to avoid damaging it.
There are a number of ways to boost or reduce a player's levels of personal investment.
Player investment tends to come with time as attachments form over the course of gameplay to both their characters and those around them. This is one of the reasons why games like the World of Darkness often encourage the use of a prelude. A good prelude strikingly draws the mundane world to which the latter insanity will forever be compared (hence making use of the 'corruption of innocence' and the 'subversion of the mundane themes') and will also give players a chance to get to know their characters and, hopefully, get attached to them before all the terrible events come to bear.
The right protagonist choice is also very important. Help each player make a believable, engaging character that they would enjoy roleplaying. Try to ensure that each person can fulfill a niche so that they don't get bored or frustrated. Reminding them that they're creating a victim, not a hero, can also re-set their frame of mind and enable them to grow fond of their characters for surviving rather than being irritated that they're not kicking ass and taking names.
Draw vivid and three-dimensional Non-Player Characters (NPCs) as the depiction of NPCs and their reaction to surrounding events is a powerful tool. Players generally enjoy taking risks with their characters' lives which, in a horror game, might lead to either an irritatingly high mortality rate that frustrates them - or a growing sense of safety as they consistently survive their risks. Having a trusted and respected NPC grow frightened, suggest caution, or even flee for the hills can often show the players a new perspective and highlight the danger without the need for a single maiming to occur.
Compelling and engaging NPCs also assist in immersion, allowing the player's a sense of a rich and compelling world. Just as players may fear for well-liked characters in a book or a movie, so will they likely fear for a well-drawn and interesting character. Foster these attachments by avoiding the death of well-loved NPCs where possible and only killing them off at the most opportune moments, and even then, only rarely. If they die too regularly, players will become jaded and will avoid feeling any attachment to them. It is best that the protagonists either get the opportunity to try and save them (with a risk of failure) or that they die in similar ways to the protagonists - by the hands of fate and some unlucky rolls.
Do feel free to put the favorite NPC in jeopardy. Just don't do it so often that it becomes trite and cliche.
Do feel free to kill off the average likable NPC. Only well-loved recurring NPCs deserve increased odds of survival.
An easy way to find sources of recurring characters is to give names and faces to those identified in their characters' backgrounds, or in the World of Darkness (WoD), by turning social merits like Retainers and Allies into people. These should ideally be the best sources for well-loved recurring NPCs but you really can't tell with players. They might end up preferring that walk-on bartender you invented on the fly as a bit of local colour over their own character's pain-stakingly drawn wife.
Players are notoriously curious creatures, which can cause them to bravely take careless risks rather than act with the caution of a nervous player frightened for their character's 'life'. Use this curiosity yourself to motivate that caution and fear. If possible, create a personal plot arc for each character that intrigues the player so that they're desperate to know the ending. If they lose their character in the general story plot, they'll never find out what happened to their sister or what that relic might do if activated.
In line with this, if their character dies and the players asks what could have happened or did happen, resist the urge to tell them. Make them stew on it. They'll worry more next time. If you really want to tell them, give it six months and make a show of how you wouldn't generally do this, but... etc.
Basically, a player knows that they can simply create a new character so the loss of a character, per se, isn't much of a threat. So make that loss matter. Whether that is the loss of an interesting relationship (platonic or romantic), an engaging NPC, a story arc, or the ability to answer a vital question, is irrelevant. All that matters is that you create something the players are afraid to lose, and then put that in jeopardy on occasion.
Oh, and don't worry, I'll discuss how to create engaging and sympathetic characters later on. In the meantime, you can always pick up a How To Write book and flick through to their chapters on characterisation if you'd prefer.
So, how do you all boost personal investment in your games?