Ah, the age-old question! I wish I knew the answer, but from my experiences talking to people and playing games, I'd say these things tend to be most common on people's lists:
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Story - Like you guys said, people want a good story. Otherwise, what's the point of the game? Well, unless it's an H game, but I assume that's not what we're talking about here
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Cute/Appealing Graphics - If not for this, we might as well read a book, right? And who wants to do that?!

I remember hearing someone describe cuteness as a quality that makes you just want to hug and protect the person...maybe snuggle up in a non-sexual way. People are drawn to cute things, and they make great merchandise (plushies!)
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Surprises - If the player can predict the story, it isn't much fun. People are delighted by amusing twists of fate. Just make sure the surprise fits in with the game somehow. Don't have aliens abduct the love interest when she's about to pour her heart out, unless there's been some reference to aliens or UFOs before. Otherwise, people will think "uh...yeah, that was dumb."
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Novelty - Do SOMETHING in your game that you haven't seen done before, or try to improve on something you have seen done before. Don't just settle for making a stripped-down version of [insert popular game here].
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Decisions - Since it's a game, it needs to be interactive. Once again, if it's not, we might as well be reading one of them "book" thingies. I think the important thing here is that people want decisions that matter! They don't want to have choices A and B, choose A and perform B anyway. You see this in RPGs a lot, like when the hero is asked to go on a mission or become leader of a group. No matter what you say, you end up being drafted into whatever decision advances the linear story. I think the Gaming Intelligence Agency described this as "Communist Choice"

Let's not be communists, okay?
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Freedom - This kind of goes along with decisions, but it's more broad. Let's take Tokimemo for instance. A mere decision would be choosing to give a present to either Shiori or Ayako. Freedom would be having the option of ditching the school completely or being able to whisk them away on a surprise date. I guess freedom is having a wide variety of options that lead to fairly different places. However, you don't see this a lot because it creates more work for the game creators. All the plot branches it leads to could be a headache.

One compromise I see is to have the plot branches, but have all the branches tie back to the main linear/general plot line at some point. From there you could make more branches and tie them back in later again. One big potential pitfall, though, is to have so many branches that each of them becomes shallow and makes the overall story suffer.
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Fanservice - While not absolutely necessary, it generally doesn't hurt.

Let's face it: we're working with cute fantasy girls (or guys) and it's all in good fun, so why not? As long as you don't overdo it (unless you're planning to make a naughty game like Myriad Knight

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I'll use the apple tree incident from ToL 1 as an example of having decisions, story, and fanservice work together. If your character has been sexually focused, he gets the option to pull Miko's pants down (decision). However, if he hasn't been sexually-focused, that idea wouldn't seriously cross his mind since it doesn't fit with his personality (story). And if he does pants poor Miko, we see her cute pink cherry panties (fanservice). A couple things to note here: First of all, no one is forced to take the fanservice option. It's up to the player. So if players don't want to see that kind of thing and see it, they have nobody to blame but themselves. (In other words, they can't blame YOU

) And second of all, the fanservice incident helps with the story. We see Miko and the guy's reactions, as well as... another cute side of Miko, all of which adds to the story and characters.
Whew, that was a mouthful, but that's what I have for now.
