It's hard to word, but what champion's playstyle best represents their lore?
For me it's got to be Talon, when you go in, it's win or die. You get one shot, just like his life on the streets must have been.
Syndra takes the cake, at least for the mage role. She's a power hungry mage with dangerous amounts of pride, and her magic is powerful enough to cause massive AoE control+damage, while obliterating whichever target she chooses. I honestly cannot think of another who plays very much like their lore, not as much as Syndra.
I really like Aatrox in that aspect. Diving into the enemy team, feeling that your life is tied to how much chaos you can create and how much damage you can deal - he really captures his concept well, I think.
Malphite. The guy is rock solid and absolutely nothing stands in his way. One of my favorites.
Honorable Mention goes to Draven for all his showy mechanics.
Tryndamere.
Veigar, his lore is about how he seeks out master mages of black magic to grow more and more powerful so he can bring the world to his knees. His power grows as the game goes on, and late game you can one combo a tank (why are you focusing a tank though?).
Aatrox is also a great example, his whole kit is surviving through fighting, just like he encourages armies to do so.
With his new passive, i think Viktor also fits very well.
riven. shes a young girl who goes into battle headfirst and gets blown up without applying any damage because shes outmatched by other enemies who have poke, range, better base stats, and better dueling.
etc etc.....
Ooooh, this is a good question. There's a ton of good choices. I'll refrain from mentioning the ones already used in cinematics.
I'd say the best are Thresh and Hecarim. Seeing Thresh throw his chain out reminds me of his log-in music. Imagine how horrifying that would be in the woods at night. Hecarim, because your goal is to rush the enemy at full speed and make them scatter. 
+ 
= Playing both as tanks and knowing that as soon as you make a move, all hell will break loose makes you feel like a Shadow Isles monster!
Jinx/Vi pair and the Jayce/Viktor pair are worth mentioning also. You can't beat the classic cop vs. criminal or the superhero vs supervillain scenarios playing out on the rift.
