The queen is a powerful spell caster. It has the ability to eliminate specific units at a decent range. It is also a fast air unit making it a good scout. Parasite is by far, one of the best scouting spells in the game. And ensnare makes your other units superior to your opponent's.
Since the Zerg require so much gas, it may seem hard to produce queens, however they are worth the cost. They are only unit that can break into a well defended base of any race. Use them to take out any dangerous units as tanks, templars, and lurkers. This is the main purpose of the queen. It'll save you from wasting your units trying to bust into a base the hard way.
Queens second purpose is to scout. Not only do they have parasite, which allows you to see the map, from you opponent's view, queens are very fast fliers. Leave them above cliffs, or at expansions to watch over the map. Use broodlings to scout the map.
To counter mass unit, the queen has ensnare, which will decrease the attack rate and speed of the units caught. It will also reveal any cloaked units. Use ensnare to stop stimmed marines from attacking you, or to slow other mutalisks and hydralisks. Try to combine ensnare with scourges to make it easier to destroy fast air units.
Acquiring infested Terrans is a rare opportunity. Infested Terrans are great for taking out workers or masses of melee units. Use them to burrow at key areas as expansions.
