I understand that some of the events would take time to create, code, and test. Keep in mind that these are simply suggestions and they can all be tweaked. Some of these events you may have already heard of, some maybe not

Hunger Games

Requirements: Level 3, empty backpack, 100% fatigue
Notes: Levelling while in the event will be an automatic disqualification.

Event: Custom made arena maps with altars in them. Upon start of the event, items (beginning with bronze armor/weps and cabbages/bananas) will spawn. As the event progresses, more items (such as longbows, bronze arrows, runes [air and mind], air staves, iron weapons/armor, higher tier food such as trout) will eventually spawn. Last player alive wins. Teaming is allowed and encouraged, just know that your closest teammate may eventually be your biggest threat to winning.

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World Boss/Events

Requirements: Differs from boss to boss; general idea is high level combat, skills, food, gear, potions, multiple people
Notes: The world bosses that spawn will always be in P2P zones to prevent people from luring them to normal afk/staking areas (such as Edgeville) except for Wilderness bosses. They can also be placed in a type of arena that people can access. These bosses will have high combat stats, drain prayer, and extremely high HP. It should be very difficult, if not impossible for someone to solo the boss. Killing a boss will reward a very high amount of experience in regards to what was needed to kill the boss. A few boss ideas:

Skar - The alpha of the alphas, this wolf returns to its lair on top of White Wolf Mountain to bring back the prizes he's earned from the adventurer's he's killed to his den. This wolf is very adept to close-quarters combat, but has a tough time against magic users.
Possible loot: Same as KBD, plus noted high-level potions, noted sharks, noted magic logs, noted dragon bones, and noted runite bars.

Enraged Ent - This overseer of the nearby forest will spawn in a forest to hunt down adventurers seeking to chop the trees in that forest. Adventurer's must work together to chop down the Enraged Ent, as well as stay alive. The Ent will attack anyone in close vicinity. The Ent does not take any physical damage - all damage must be done by chopping the Ent down (such as with a normal tree).
Possible loot: When killed, the ent will drop noted yew and magic logs as well as however many logs was given in the process of chopping down the Ent, dragon hatchet (if custom equipment is intended later on).

Merle - Merlin's evil brother, Merle, has escaped once again from his magical prison and intends to wreak havoc on the world. Merle will cast powerful magical spells at random targets and has incredibly high defense. It will take multiple adevnturer's to stop him.
Possible loot: 10000 air/fire/earth/water runes, 5000 of all other runes, possible custom high level magic equipment (depends if there are plans to implement custom high level equipment later on)

Drov'vok - AKA The Death Bringer. He returns to his icy lair on top of the Wilderness Frozen Waste Plateau, surrounded by his Ice Giant, Ice Warrior, and Ice Spider minions. Those who manage to kill him and escape the wilderness in one piece are able to sell his coveted head for a million gold pieces (only one head may be held on a character at any time), as well as have a chance at high level combat gear. Do keep in mind that the death bringer isn't only known for the deaths he cause, but the ones that are caused around him. This is high level wilderness - expect trouble. Oh, and one more thing - magical pools refuse to allow you to filth their waters with the Head of Drov'vok. You must run out of the wild yourself if you have the head in your inventory. The head is untradeable.

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Lottery

Requirements: Enough gold to buy a lottery ticket
Notes: Ticket costs can be anywhere from 50k-150k a piece. Users can purchase an unlimited number of tickets for the lottery.

Event: Lottery event message displays every 1-3 hours. Users can purchase a lottery ticket by using a command and paying the appropriate amount of gold for it. People can purchase an unlimited amount of tickets, thus bettering their chances in the lottery and upping the pot. The jackpot is the entirety of the money put in, minus a cut the server will take (basically a slight gold sink, say 10%).

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Scavenger Hunt

Requirements: None
Notes: Items need to be random, tradeable, but possible for all characters to obtain. It's okay for it to be difficult, just not impossible. I would lean towardItems cannot be gated behind quests.

Event: A list of items (12 total) will need to be obtained from various locations throughout the RuneScape land. A good item is something that is considered, tradeable, easily obtainable, but somewhat of a "challenge" in order to acquire and not easily found in the AH. For instance, a bucket of milk isn't often found in the AH and would require finding a bucket and milking a cow in order to achieve. It's usually best to have 6-8 easy to obtain items, 4-6 with medium difficulty, and 1-2 hard to obtain items. After obtaining the items, the first person to trade the event handler ALL of the items AT ONCE will win the prize.

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The Amazing Race

Requirements: None
Notes: Food recommended for lower levels

Event: Custom maps or in game content can be used for the race. Players will start at one point of the race (preferably behind a closed door) then make their way through a course to reach the end. The first person to reach the end of the course AND trade the event handler will win the prize. A perfect location for this would be to start at the Champion's Guild south of Varrock, then make their way through the Varrock sewers to the ladder at the bear cage. Another great place is the Observatory maze.

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Down & Back

Requirements: Level 3 account, empty inventory, 100% fatigue
Notes: This is a variation of a survival event, where players will begin on one side of an arena. The arena should look like a simple, rectangular area that is in the wilderness. The initial spawn area will not be in the wilderness. A master fisher should be placed inside the spawn area. Upon entering the arena, you are automatically skulled. This ensures that all items will drop when killed. Items must not be able to be taken into or out of this event. Multiple people (max 3) can win this event. People may re-enter this event upon dying. Non-level 3

Event: In the middle of the arena will be monsters that are stuck behind bushes. On the other side of the arena are up to 3 items on the ground (same item, make it random). The object of the game is to reach the other side, grab the item, and make it back to spawn area without dying. There are a limited number of items on the other side and when they're gone, the only way you can get those items is by killing the players with it. When the event moderator says "Go!" the bushes will be removed and the door to the arena will be opened. Immediately inside the arena (next to the spawn area) there will be iron weapons/armor spawned that players can opt to take to kill the players returning from the other side. Once all 3 items are brought across, the event is over.

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PvP Arena

Requirements: The event's established leve of character (33, 46, 61)
Notes: All types of pures welcome, just don't be surprised if your defense pure becomes a target

Event: All competitors will enter the event area. No fighting may take place prior to the start of the event. People intentionally attacking others prior to the event will automatically be kicked from the event. Once started, fighting will commence. There is no altar for prayer here, so be weary of your prayer points. Last contestant standing wins. The event reward is the loot from all other combatants, which should be getting picked up by the moderator. Do keep in mind that stacks of items from fallen combatants will show, which is the only way to replenish your food/arrows/runes. If there are no real drops from combatants, it is at the moderators discretion as to what prize is rewarded to the winner (gold, typically).

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That's all I have currently. If more events come to mind I'll update this thread. If you have any events that you'd like to add - feel free to do so and I'll update the list with your name on it.