I believe Custom Games have an untapped potential. By giving players ways to customize their match, we can get a variety of fun ways to play. I have thought of some myself and I believe they will give the game more diversity when it comes to matches.
* Set Starting Gold: This would give a bunch of different ways to play, either by going in with enough gold for a full build, start with just enough gold for a full set of boots, or even starting with no gold forcing players to farm (thus improving their CS).
* Set Starting Level: Combined with the previous option the realm of different ways to play increases, either by having a bunch of level 18 champions in The Howling Abyss with no items or having a team start with a head start. This option also allows player to practice things like late game strategy without having to play an entire match.
* Set Starting Turrets: This option allows players to practice things like comebacks or just play for fun having a handicap to see if their opponents can beat them. A possible way to allow players set this option is by giving the player a map with all the turrets marked on it, the player then can click on them to disable/enable them as he sees fit.
* Enabling/Disabling basic items: Imagine a game of hunt or be hunted in the jungle. One player has to move through the jungle trying to get as many kills as he can whilst being hunted by 3 other players. By disabling items like wards or potions the players must find the target with no way of healing or having any way to find the opponent without engaging. Along with the Starting Level/Gold, you can have something akin to Evolve. This idea is more for when random people join your game, through this you can guarantee everyone will play by the rules.
* Setting Minions per Wave: Minions are more than meat shields for turret destroying, they are income. By reducing the amounts of minions per wave you also limit the amount of farm people get, forcing a more aggressive/defensive play style since your only reliable way of getting gold and XP is now your enemy.
These are just some ideas, feel free to share your thoughts on them as well as suggest more.