Which champions (when learned) make you better at the game in general?
 

Champions who can help you get better in a variety of areas, such as positioning, kiting, last hitting, skill-shot landing, mechanical skills etc.

I'd say a few examples of some of the better champions for teaching the ADC role is Ashe. She taught me how to ADC properly with kiting and a "base" simplicity of sorts to help me learn from the ground up, and also her ult improved my prediction skills.

MF taught me about positioning and prediction skills.

Who else? Who helped you guys learn?

Katarina taught me to go in at your own will. Only fools hesitate.

I sir am no fool.

Nidalee top lane and Amumu jungle.

Teaches you everything.

lee sin taught me how to be situational

Prolly gonna get downvoted to all hell for this one, but..........

Teemo...

Placing shrooms all over the map showed me how important map control is, and taught me its important to ward those places when I'm not teemo. I may not be able to slow and damage them with a ward, but can at least see them coming.

Ahri...

Syndra. You learn positioning is everything.

Eve taught me to gank.

Draaaaaaaaaaaaaven

LeBlanc and Ryze helped me learn the importance of smart-casting combos.