For instance, how many times have you watched a sports game (seems to be the most obvious in basketball, and hockey I guess) where a small foul sets off a hack-fest between both teams throughout the rest of the game? This usually happens in the playoffs. Emotions are tense and get the best of the athletes, and what starts as just a semi-intentional whack on a layup turns into shoving in the post, off-ball fouls, and some verbal jarring between both teams, which really gets the crowd screaming and yelling.
I really wish video games could display this emotion just like it is in real life. I can picture it now in 2K10 or Live 10 - a "hard foul" at some point in the game, a cutscene of the two players trash talking, then the next set down the court there's obvious pushing/shoving/hooking in the post, the crowd starts screaming, and a foul is called. The play gets rougher, the home crowd's reactions are louder, and the refs quit calling the light fouls and focus on the serious stuff. Players dive for balls and fight harder for possession, timeouts are called in attempt to settle the players down, maybe refs even warn coaches after a particularly rough play. Players and/or teams could be rewarded skill-wise for keeping clear heads under the pressure.
Having this sort of emotion in a game, especially in the postseason, would be huge. It could probably work for hockey too, and even football - we've all seen it happen on TV and with that much emotion carrying on throughout the game or playoff series, it would only feel even more realistic.