Story and Character

Personally, I've never really been interested in the characters or the story of a game. I've always been interested in the environment the games are set in. However, characters and stories cannot simply be ignored, as without these, most games would be rather dull. Let's take Assassins Creed for example. The basic structure of the game is to simply go around stabbing dudes in charge of less important dudes. However, whenever you kill a dude, they tend to give you rather a lot of information, how they are related to the other characters, and what effect they have on the story. If you have the patience to sit and listen when you could be running and jumping over rooftops, you begin to realise that a lot of effort has been put into the characters personality and storyline. Personally, i tend to get rather bored, although I do sit through each cut scene in a game.
Some games and their characters have similarities with TV shows and films. There is generally a plot and a bunch of characters who you get to know after a while. You find out why there are in the situation they are in, there feelings for one another and their likes and dislikes. Games like this include the Final Fantasy series or oblivion. In these games, depending on how you behave, can alter the story and the characters behavior, resulting in a far more enjoyable experience.