I shouldn't be laughing this hard.
To answer OP's question, cartoons and anime rarely affect me. One specific example was Regular Show's finale. I didn't think that a formulaic show about two furry slackers could nearly bring me to tears in its last 5 minutes, but it did.
The only anime ever that nearly made me cry was Cowboy Bebop. The weight of that last scene, and a line from a earlier episode, still sticks with me today.