Water that will not stop and cannot be shut off at the fixture itself is the clearest case: a supply line has let go somewhere behind a wall or under a slab, and every minute it keeps running adds to what eventually has to dry out.
Sewage backing up into a tub, shower or floor drain is the other one that does not wait. It usually means a main line is blocked somewhere past the house, and the fix is not something a plunger reaches.
No water at all, anywhere in the house, points to something at the main line or the pressure system rather than one worn fixture, and it is worth a same-hour call instead of waiting to see if it comes back.
A dripping faucet or a sluggish drain still deserves attention, just not an after-hours call. Knowing where the main shut-off sits, close to where the supply line enters a Cooper City house, is worth doing ahead of any of this.