Very few a/c can 'stand still' as you put it. Helicopters can, blimps & dirigibles can, specially designed a/c such as the Harrier can, and a few odd research platforms eg the 'flying bedstead' of the 1960's (date?). Some particularly powerful military fighter types and high performance aerobatic aircraft can be made to point skywards while having some amount of support from their engine's thrust but that's usually measured in moments, not minutes.
Apart from those sorts of things other a/c need to move forward through the air to generate the lift that keeps them airborne. They all have minimum speeds at which sufficient lift is produced. *IF* they happen to be flying into the prevailing wind *AND* the wind is at least equal in speed to the aircraft's speed then the aircraft would be stationary over the ground. Think of a boat travelling upstream in a fast moving river. If the river's speed is fast enough then eventually the boat will not make headway compared to the shore. It needs to be a very strong wind for an aircraft to make little or no headway.
The options used to delay progress of an aircraft include reducing speed (but there's a limit to how slow any particular aircraft can fly), not flying directly towards the destination - which will delay the eventual arrival time - or to 'hold' by flying circles or racetrack patterns over some area until the need to hold is no longer present.