My fandom kind of varies. Generally I will become a fan of a team if they have players showcasing a particular playstyle I like. I really liked the way C9 played the map in the past and they played a really smart game, so I instantly became fans of theirs - and I will always root for them, even when they have a hard time.
Sometimes as you get to know players or see their behavior you become a fan of a particular individual. I am not a TSM fan (though I will back them at worlds), but I cant help but like Lustboy's support style. He has some great highlight plays, and although he is really confident in himself, he's a really good sportsman to the opposing team at the end of each match.
As you watch the teams develop over time, you will find a favorite among the stories that play out. Just look at Gravity for example. Nobody knew that team 2 seasons ago, and they looked like they were little more than the last hurrah of semi-retired veteran SaintVicious. He leads them into the LCS out of Challenger, they have an average split, and Vicious subsequently retires, handing the leadership reigns off to their support BunnyFuFuu.
And what do you know, the kid's shot-calling is aggressive and decisive, just like his personal playstyle, and all of a sudden, Gravity becomes a team that can beat anyone in the LCS and is now a contender for Top 2 or 3. Teams know that Gravity is always looking to go for the throat and now they are knocking on the door of all the top teams - its anyone's guess how far they are going to take it.
So I guess it depends on the stories you find. Personally, I am a huge fan of Gravity right now. Their story is too awesome to ignore.
SaintVicious stepped down, and in doing so, he created a team more powerful than anyone in the LCS could have imagined, making BunnyFuFuu the freaking Luke Skywalker of LCS.