There are large varieties of custom games…
Hero arena - Each player has a hero. Try to slay the heroes of the other team.
Gladiator - Monsters will occasionally appear from a portal. To win, you must survive all waves.
Tower Defense - You must build a variety of towers to defend a certain spot (often the middle).
Tower Maze - A game based on Tower Defense. You must build towers in the shape of a maze to defend a certain spot.
Strife - Two teams automatically engage eachother. You have only one hero to help.
Life of a Peasant - Live your life in a city or village.
And, of course, there are Role Playing Games. I don't think I should explain what that means?