I own every champ in the game and I've played them all to a fairly ridiculous extent, as one might expect from someone who's played the game since beta, but I'm very partial to three in particular at the moment.
Wukong is just a champ I've always clicked with. His burst is ridic, his itemization is incredibly easy, and his potential for game-changing, unbelievably funny jukes is up there with champs like Leblanc.
Karthus, because I was watching him in the IGN IPL5 2 days ago and decided to give him another shot, since the last time I played him I was absolutely dreadful. Think I ended up going like 18-7-15, after my team gave me shit for playing him thinking I was going to be awful again.
And finally, Varus. Just, so damn cool. He's the only champ with a backstory written by an actual decent writer, he has a ridiculously cool model, a great voice actor, badass dialogue, and awesome animations. Not only that, but I clicked with him the second I played him. Harrassing with autoattacks, throwing out blind arrows for max range kills, he's got a heal reduction, he's got a slow, he's got a stun, he's got mad auto-attack damage thanks to W and his passive, he's got tank killing capabilities, and he's got SILLY burst.
But no one plays him. Which I'm fine with. Just means people don't know what to do when I come out as him and carry yet another game.