Some creatures have a fly speed. Some creatures with a fly speed also have the ability to hover specified.
The PHB, in Chapter 9: Combat, Movement and Position, Flying Movement says:
Flying creatures enjoy many benefits of mobility, but they must also deal with the danger of falling. If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as by the fly spell.
The conditions in this paragraph that would result in the creature falling have to do with having movement involuntarily removed or restricted. That might suggest that if you don't have "hover" in your flying speed, you can't hover.
But there is a difference between being knocked unconscious, or frozen, or webbed, or otherwise rendered unable to move, and choosing to stay in one place while airborne, by flapping your wings, or standing on your jets, or whatever.
So, can flying creatures choose to stay in one place while airborne, even if they don't have hover in their flying speed?
Flying creatures can remain aloft unless their rules says otherwise
The 2019 Sage Advice Compendium contains the following paragraph which directly addresses this situation:
From the Flying Movement section under Movement and Position (PHB, p. 191) we have (emphasis mine):
Possessing the 'hover' ability prevents a creature from falling when knocked prone or deprived of movement, but otherwise has no effect on where the creature may end its turn. By default creatures that possess a fly speed may end their turn in the air. However, doing so without the 'hover' ability exposes them to falling damage should an enemy somehow deprive them of movement.
Some creatures or abilities may limit your flying ability and require you to land at the end of your turn. See Do I have to land at the end of my turn? for evidence that this is not the general case. One example of a feature with this restriction is the level 14 Path of the Totem Warrior (Eagle) feature which says (emphasis mine):
If the feature allowing you to fly does not possess text to a similar effect, you can end your turn in the air or remain stationary while aloft. Having the 'hover' ability merely negates the risk of falling.