Characters in games are, for me, the most important aspect of a good game. If a game has a good, developed, intriguing main character, the graphics especially, don't really matter, for me anyway. Games like Metal Gear and the big games series tend to have well developed characters that grow over the X amount of games. Solid Snake is my all time favorite character. Not only because he is a well developed character in my eyes, but because the voice acting for him is some of the best I've experienced in the video game genre.
The techniques used to attract audiences to certain characters include the voice acting and personality of the character. Recently, playing Left for dead 2, I found that even though most of the story is told in-game, it's a great way to get the player interested. Long have the days gone where the player had to sit through hours of cut scenes. Now the player has no choice, they have to listen to the story whether they want to or not.
I also think a well designed character is appealing. In L4D 2, all the characters a varied in appearance, have different back stories, and are designed to be appealing to different players. Even though the character does not affect the gameplay, I still find myself attracted to playing certain characters. Coach, for example, is my favorite.
I definitely think games of the next generation will be geared towards the story aspect. Like Randy Littlejohn said, players will want more than a generic story line and boring story line, even if the graphics and special effects are out of this world. I predict games and films will become more closely related. With top directors and screen writers merging with game developers to create entertainment that is on a completely other level.