For me it's the rivalries that build up in your mind in fictional leagues, and how they play out.
The Charlotte Blue Sox lost to the Calgary Stampede in three straight world series' in an NAL game I'm running (to prepare for my first dynasty report game

), only to eventually win their first ring against the Leon Kings a few years later. In my head, they're not satisfied until they beat Calgary for the championship. No other rings matter to them.
To make matters worse, their star SP was MVP in two of the three championships, but was out for the season when they won the ring, so he doesn't have one. Feels bad, man.
That type of thing is why I play OOTP.