The Zerg have many common attack tactics. Here are just a few:

Speedling Run-By
Zerglings with the metabolic boost upgrade are easily the fastest unit in the game. The upgrade allows them to quickly dart past a deployed army and strike at vulnerable locations. If your opponent fails to build enough static defenses at an expansion or leaves a gap open in their base, your zerglings can run right in and cause a great deal of havoc – forcing them to pull their main army back to deal with the cheap zerglings.

Baneling Bust
Banelings are extremely effective at crushing through weak buildings, such as supply depots or pylons. If you morph several banelings to bash through a wall of enemy structures and flood their base with zerglings or roaches, they may be unable to deal with them. Protoss players in particular tend to skimp on units early-game to research technology aggressively. Be sure to force them to stay on their toes.

Be warned that this technique is usually considered an “all-in” – a failed bust will usually leave you without the infrastructure or economy to keep pace with your opponent, and you’ll be fighting an uphill battle from then on. Don’t only commit halfway.

Roach Hit-and-run
Roaches can attack, burrow, regenerate, and then pop up again to continue fighting. They regenerate quickly when burrowed, and can travel while underground. If your enemy doesn't have ranged units or detection, skirmishing with roaches can be very devastating.                                      

A Zerg player slaughtering a Protoss base with Roaches.

Infestor Sharking
Infestors have the ability to throw infested terrans while they’re burrowed. They can sneak around the map undetected and drop their terrans where they’ll deal the most damage – such as at an undefended expansion or a line of siege units.

Overlord Drop
Grab some overlords, fill them up with units, and drop those units on an enemy base to circumvent their army and static defenses.

Here’s the drop-off.
Overlords drop roaches at a defensive choke point.	A zerg overlord drops banelings on enemy targets.