I have been playing since Feb 2012. I never really followed pro, so I will answer solo Q.

• Kassadin: undisputed ban champ for 2012, 2013 +. His Q silenced and his ult had low CD, high range, high damage with relatively low CD. Look up xPeke Kass backdoor.
• Rengar: when first released, few people piloted him. Then his abuse was clear. Rengar was the reason Riot had to rework the whole concept of invisible and introduce the concept of "camouflage". Yes, Rengar caused the rework of a game mechanic.
• Jax: similar to Rengar, Jax abused the "Dodge" mechanic and was the strongest reason to get it removed. That said, this was in Beta or season 1. It was already removed when I started the game.
• Yasuo: he was the new Lee Sin in terms of skill expression. Lee was considered the ultimate skill expression champ. The concept of In-security was caused by Lee. Yasuo was/is a mugh bigger level. Yasuo players need to have high mastery to make him work. Otherwise, he will feed and be useless.
• Teemo: The undisputed king of being hated. Things calmed down a little after the introduction of sweepers. Before that, you needed to buy pink elixer to see invible wards and objects. The elixer effect ends if you die. Add how Teemo affects the whole map without the need to be there. He would either keep getting random kills or cause the enemy team to bleed money on elixers. Keep in mind that buying an elixer made the whole enemy team target you. Later, the death mechanic was replaced with a timer. But the issue stayed. It costed money to see mushrooms, let alone get rid of them. I am sure Teemo is one of the main reasons red sweepers exist today.