When it comes to emotionally involving media (any form), the trick is to not to make it happen to the player, or an audience member, but to make it happen to the character that the player or audience has identified with. For instance, lets pick a fairly superficial movie for which I'll have no problems with spoiling.

Armageddon.
The scene when Bruce Willis's character, Harry, has decided to stay on the asteroid to blow it up and has his good-bye talk with his daughter Grace, played by the adorable Liv Tyler. The movie itself is criticized for being fairly shallow and cliche', whatever, but what it does right thats completely transparent to most people is it goes well out of it's way developing the characters and relationships between them. So, when Gracie, a character whose central to the story and a point of identification for most of the audience, realizes that her Daddy is going to die, everyone in the theatre will react to it as a matter of either basic human empathy, or a bile in your throat, depending on if you're a bad person or not.

So, the lesson for game design is if you want to convey emotion to the player, you have to emulate it between the characters and make sure that its authentic enough that the player develops an identification and attachment to his characters.

On a side note, anyone get a reaction out of Chrono Trigger, the scene where Crono dies? Its not because crono dies that you react, its because Marle had to suffer the lost of her best friend that you react.

Personally, I feel greater emotional involvement from things that 1) are not mandatory or force-fed, and that 2) are or at least seem to be under player control (and not in cutscene-universe).

For example, I think it lessens the feeling of curiosity in Unreal2 when on the alien planet mission, you explicitly get side-objectives to investigate the aliens' experiments. In contrast, no-one tells you to examine the translator logs lying around in the original Unreal.

Another example: compare the PC - NPC "romance" in say, JK2: Jedi Outcast and Doukutsu Monogatari (Cave Story). In the former it's forcefed, predetermined and happens mostly in cutscene space, in the latter it's optional (at least after a certain point), dependent on player actions, and severely underplayed. Guess which I felt more connected with?

I think the interface also matters quite a bit. For example, Deus Ex has tons of conversations, but not much of "cutscenes" as such. The conversations aren't just for passive watching, as you often need to make choices, or are under gunfire while receiving some info :) In a way, the player is thus kept "in the game" at all times and may likely get more involved. But if there have to be cutscenes, I'd say in-engine are better than binks: you may feel more connected if the representations of characters & places don't suddenly change.

In line with doorstop's thoughts, I'd find it optimal if a game had emotional depth for those who want it, but would not try to force it on those that just want to focus on the pure "gaming" aspect. But can there be too little forcefeeding? After all some complained that there was no story in HL2 :)

Chrono Trigger <- Agreed, though it was upon his return. Very moving. Wish I felt that way about the ending... Lavos was a faceless and almost unnecessary villain.

[nitpick]
And aren't 2-D characters considered moderately well developed? They're no novel protagonists, but they have some development and an 'area' of multiple characteristics. A 3-D is what you want I think, having an 'area' of characteristics, plus some 'depth'. The pure 'stereotype' characters are considered one dimensional, not two...
[/nitpick]

I agree that characters are the only way to appropriately convey emotions. If you expect to get a reaction from the player, simply telling them of something in the story isn't going to do it. That's like the news, it's a passing glance at an event that doesn't really have a face or a name or any way to connect with. It's when you hear of its effect on actual people and how they react that it becomes actually emotional.

Example:
- Event
a) Your main villain goes out of his way to kill a fluffy kitty.
b) Your main villain goes out of his way to kill a fluffy kitty that belongs to a poor orphan, and it was her only friend.
- Reaction
a) Meh, he's a prick.
b) I'm actually feeling very sympathetic and sad for this orphan, who already has such a rough life... she didn't need her innocent kitty friend taken away.

You can work with b) to further plot or develop character, but a) is bland and without purpose. Connect to characters, and work with that. Don't just force feed players events that are supposed to have feeling.

There could be deeper reasonings to option a), perhalps he's fighting his own inner demons, and what may appear as some random act of violent agression could lead to deeper understandings later on, or as a subtle clue for people to hate him or associate him as a tortured individual, depending on how he looks when he does it. Your more likely to get that kind of reaction if a child kills a fluffy bunny rather than an adult, somethin's gotta be wrong if a child does it. ;D

I think visual representations of emotions ingame can hold a powerful impact as well, just look at the Silent Hill series and its representations of Evil, or the cutsy factor of Klonoa 2, Threads Of Fate, and other anime titles that kids like. Pokemon/Digimon should probably be mentioned, god knows kids couldn't seem to get enough of those.