It drones on and on and on and on.
Remember that every time you build a structure you lose one drone.  Make sure you always have ample supply.

Overlord Oh Overlord.
Zerg are the toughest race to keep ahead in empty unit slots because you can produce 3 or more units in one crack at a hatchery.  Keep an eye on your unit levels and always have excess overlords on hand.

Gurgling with Zerglings.
Burrow zerglings in the empty expansion slots on the map.   When you enemy tries to expand you wait until he/she spends the minerals and then hit them hard.

Zerglings can also be used as cannon fodder while your ranged units attack from a distance taking out the enemy.

I've been defiled!
A combination of defilers and mutalisks can be a formidable offensive force.   The defilers cast plague on the enemy and the mutalisk triple attack wipes them out.

Killer Recipe
A wonderful combination of units is as follows;
A dash of Guardians (5-6 is a nice number)
A pinch of Mutalisks (12 or more works well)
A smidge of Overlords (2 is perfect)

Bake as follows:  The Guardians can take out any ground units before the ground units can attack them.  Try to attack from hills so ground units cannot get very close and you can run away.  The mutalisks take out any air units that annoy your Guardians.  The Overlords detect any cloaked air units.  Simmer the enemy's base and stick a fork in him.  He's done.

You parasite.
The queen's ability to parasite an enemy unit is very valuable.   Placing a parasite on an enemy unit shows you what the enemy sees. 

The scourge of your enemies.
Scourge are excellent anti-air units.    Have them patrol the perimeter of your base.

Scourge also make excellent air cover for your guardians.  They cannot attack ground units however so make sure you also have mutalisks around to mop those up.

Do I detect an attacker?
Overlords act as detectors of cloaked or concealed units.  Spread them across your perimeter as early warning beacons.

Burrow zerglings at chokepoints of the map as early warning radar.  The enemy will no longer have a surprise advantage.