Fools' Errands and related varieties...

A fool's errand is a task that cannot be accomplished because of fate or because it is a joke. It comes mainly in two varieties: trying to find something that does not exist, or trying to accomplish an impossible task. Others who are aware of the prank will often redirect the victim to several different places.
The prank often involves the use of jargon, where the immediate meaning is not obvious. It can also depend on a new recruit's unfamiliarity with the business, such as being sent on a search for an ID10T form (IDIOT).
In carny, a type of fool's errand is known as the key to the midway.
[edit]Common items
Homophones: long stand, long weight (wait), or a long felt want, shoreline. In the Air Force, some activities such as gathering "flight line" or a bucket of "prop wash" have similar purpose, sending someone out for a bottle of "K9P Lube" (Canine Pee).
Machinery parts that sound real, but if considering the actual machine, cannot exist: muffler bearings, diesel engine spark plugs, piston return spring, canooter valve, headlight fluid, or a top/bottom radiator hose for a Volkswagen Beetle (which happen to be air cooled and therefore have no radiator).
Tools that do not exist, such as a metric adjustable wrench, 3-foot metre stick, shelf-stretcher, board stretcher or left-handed versions of usually achiral tools (wrench, hammer, or screwdriver), or tools made out of unlikely materials such as hammers made of glass. Often times this is switched to where the tool to be used is real but the task is not, such as the Army prank of making the object of the joke tap armor on the side of a vehicle with a hammer to check for 'soft spots' by sound.
Fetching a quantity of something that can not be contained, for example, a bucket of vacuum, a bubble for a spirit level, steam, flight, or shore line, striped paint, prop wash, or sparks (especially sparks from a grinder).
Things that have no physical existence, such as telling an orchestra member in whose part is written tacet to "go find the tacet" as if it were a musical instrument.
Items that are patently ridiculous (such as striped/camouflage paint, dehydrated water, or a box of nail holes) or figurative (such as elbow grease).

FROM WIKIPEDIA