Something that irks me is when people use "rival" when they mean to say "enemy." A rival is, by definition, "a person or thing competing with another for the same objective or for superiority in the same field of activity." An enemy is "a person who is actively opposed or hostile to someone or something." An easy way to see if they're rivals or enemies is the simple question, "do they want to kill the other one?" If yes, they're an enemy. Rivals, on the other hand, simply force the other to become better by competing with them, but don't want the other dead.

Example of incorrect use of "rival:" Swain's relationship with Jarvan IV. Swain and Jarvan want the other dead.

Example of correct use of "rival:" Garen and Katarina. Garen and Kat would both be quite sad to see the other die, but compete with each other.