Most items that require a drop of only a single item, such as the retrieval of a specific item, or the removal of a head from a named mob, each player in the group that loots the mob can each loot one of the items.
Quest items that require you to collect a certain number of items can only be looted by one player at a time.
The former can be looted by any questholders regardless of loot priority (such as Group Loot or Free For All), the latter are looted as normal. If only one person has the quest to collect a number of items, they may loot from each mob that drops a quest item, regardless of loot priority. They will also be able to loot any money, and start any loot threshold rolling on items whose quality is at or above the loot threshold.
There are still other quest items that drop regardless of having the quest or not. Some of these have alternate uses, others are used only for the quest they are attached to. Often they are not soulbound items, and can be traded, sold or bought by and from players.
The final Quest Drop is the drop of an item that starts a quest. Each player in the group can loot the item, regardless of loot priority. The quest item may still have a level requirement, and some quest items of this nature can be used in other ways (e.g., Ghosthowl's Pelt may be used as a cloak).
A world drop is a drop that has a random chance to drop off any mob or chest (within a certain level range) anywhere in the world. World drops are largely impossible to farm for because no specific mob or group of mobs have a more than a minuscule chance of dropping the item. While most World Drops are usually a drop of uncommon quality (green) or better, this is not universal.
Not a very widely used term, but some uncommon or better random drops are actually restricted by continent.
Example: All "Bristlebark" named set items (, , etc.) can drop off any mob within a certain level range in Kalimdor (including instances) but not in the Eastern Kingdoms. On the other hand, all "Silver-thread" armor (like ) only drop in Eastern Kingdoms.
Each instanced dungeon has its own unique selection of rare zone drops. Like world drops, they have an extremely low drop rate, can drop from any mob in the zone, and are usually bind on equip.
Example: is a rare drop off any enemy in Shadowfang Keep.
A drop that only comes from a specific mob or group of mobs.
A drop of an artifact quality (brown goldish) item. There have been no artifact drops yet.