CTF, and others

How about Capture The Flag in LoL?

Also, LoL requires a great deal of teamwork. A Missions map perhaps? Maybe each team has to work to complete an objective with the greatest effect in the shortest time (which team can destroy the most turrets, etc)?

Hide and seek maybe? Recreate our childhoods?

Paintball: One hit = One kill?

The League of Legends Equivalent of Minecraft Skyblock: Do the most with the least.

Turn-based games?

League of Legends Chess somehow?

Racecar drivers: move the champions to different objective points around the map in the least time?