If you answer 'yes' to the above, then this is possible:
- When a rogue tries to run for cover, an archer Readied to 'shoot him if he tries to move' gets his shot off first before the rogue gets to cover.
- When a mage attempt to cast an Invisibility spell, a player Readied to 'cast Magic Missile on him if he attempts a spell' gets to attack him before the Invisibility takes effect (Magic Missile spell requires a visible target).
- When a caster attempts to cast Magic Missile on a player that has used the Ready action to 'run through the door and out of line-of-sight if the mage starts casting a spell" the player does just that, preventing the mage from targeting him.
- When a dragon starts to use its breath attack, a tightly packed group of goblins that have used Readied actions to "run if the dragon tries to breath fire on us" all run in different direction, making it impossible for the dragon place them all in with the AOE of its breath attack.
Now, if you answered 'no', then that means:
- When an archer uses a Readied action to 'shoot a rogue if he tries to move', the Rogue can move behind nearby full cover and avoid being shot, thus wasting the archers use of the Readied action.
- When a player readies a 'Magic Missile spell to attack an enemy spell caster if he attempts to use a spell', the enemy spell caster can use the Invisibility spell to avoid being targeted, thus wasting the players Magic Missile spell.
- When a player uses a Ready action to 'run out of sight if an enemy spell caster attempts a spell', he will not get to move until after the spell caster has finished that spell.
- A dragon that readies a Breath Attack on a group of goblins 'if they try to run' won't be able to target them all if they run in all different directions.