This documents the ways griefers grief Minecraft servers. This is typically aimed at vanilla or modded servers (Spigot, CraftBukkit) with little to no protection.
This method is simple: Simply destroying everything in sight. Since diamond tools are easy to get with XRay, a griefer could easily do lots of damage by using diamond pickaxes and axes. Nukers are also used to grief easily destroyable things like crops.
-Building Offensive Structures - This tactic involves building offensive structures, such as swastikas or genitals, making the terrain look extremely disgusting.
-Durable (hard to break blocks) Walling - This tactic involves walling structures out with durable blocks like obsidian, which forces players to spend lots of time trying to break the obsidian. The tactic is only useful in servers where the victim doesn't have access to creative mode and OP, and can't get a staff for fast fixing.
-Repositioning - A method that is hard to reverse manually, this method uses blocks alike to the original structure (usually mined form the structure) to randomly build around the structure. This is especially hard to reverse manually because the repositioning makes it hard to figure out the original structure. It also can't be removed with WorldEdit, because WorldEdit can only replace a type of block with another block.
Lava and Water Griefing Edit
This method involves pouring lava and water, typically to create tons of cobblestone and obsidian. This is effective in cobblestone structures, as it becomes hard to remove. It also creates an annoyance trying to clear out the liquids.
Mob Griefing Edit
This method involves using creepers to blow up the terrain. Even if the creepers don't spawn in the structure, the holes created typically makes the terrain look ugly and hard to undo manually. Since structures usually contain torches to prevent mobs from spawning, smash nukers are used to eliminate the torches and allow hostile mobs to spawn.
TNT Griefing Edit
A rather difficult type of griefing due to the rareness of gunpowder, this method becomes useful if there is lots of gunpowder/TNT lying the the chests. Even more dangerous are slime TNT duplicators, because they create an entire line of destruction and are hard to reverse.
Map Corruption Edit
Map corruption used to be common in old beta maps before beta 1.8, because of the existence of far lands and mathematical errors, giving the server a huge CPU load. Not blocking high speed hacks were also a cause, as players could fly very fast without getting kicked/rubberbanded (vanilla has this protection now). Players only had to use hacks to fly millions (or even thousands) of blocks out to stress the server, resulting in the server crashing. Nowadays redstone lag machines (creating repeating redstone circuts and connecting them to blocks powered by redstone) and dropping tons of items (common in creative servers with no regulations) are the top ways of doing this, although it takes a lot of crash a server, especially ones with a large RAM. Spawn chunks (areas near spawn) are the best places to do this, because the area keeps ticking (e.g. redstone circuits keep running) even if all the online players are far away.
OP Griefing Edit
Usually targetting poorly setup Bungeecords or very rarely semi-popular servers (using short lived exploits like OP Sign or CMDBlock), this involves the player OPing themselves and then spawning in powerful tools (like "nuke" fireballs with a custom blast radius) and destroying the server. This is impossible to do currently in 99.999% of the servers, because there isn't an exploit that allows you to do so.