Drone Scouting
Like the Protoss and Terran, early-game scouting is incredibly important to avoid cheese tactics, all-in strategies or other uncommon strategies. A useful time to send a Drone to scout your opponent's base is after creating your first Overlord; this allows you time to find it and spot any suspicious strategies, like an early rush, giving you time to prepare a counter. Keep your Drone alive as long as you can. This will prevent your opponent from doing anything that will give you any information and thus set him behind until your drone is killed.
Research Overlord Speed
Once you've upgraded your Hatchery to a Lair, you can research Evolve Pneumatized Carapace, an upgrade that grants a significant boost to your Overlords' flight speed, for 100 minerals and 100 gas. This isn't only helpful for being able to scout any area on the map much faster but can also help your Overlords escape if they're being attacked; this is immensely helpful when you're trying to avoid becoming supply blocked.
Overlord Spread
The Zerg have an advantage over the other races; the Zerg's food supply units are mobile, so take advantage of this mobility. By the mid to late game you'll have plenty of Overlords, so move your Overlords to different positions all over the map to give you vision of as much as possible. If you can see your enemy coming, you'll have plenty of time to prepare.
Changelings
Evolve one or more of your Overlords into an Overseer to take advantage of its Spawn Changeling skill. This spawns a creature that takes the form of an enemy unit and therefore won't be attacked unless your opponent actively orders his units to. Because of this, you get a unit that lasts for 150 seconds that you can use to wander your opponent's base freely until they notice. This can give you a large amount of information; the best part is that it's completely free, requiring only an Overseer's energy, which regenerates over time. Overseers are also useful in that they travel faster than Overlords and can also see invisible enemy units.
Research Burrow
Research Evolve Burrow at your lair to give your units the ability to tunnel underground, becoming invisible. Burrow Zerglings at random spots on the map to get a wide view. If your enemy can't see invisible units, she won't have any idea they're being seen. Research Evolve Tunneling Claws at the Roach Warren to allow your Roaches to move while buried, useful for scouting as well as hiding/retreating. Infestors can also move while burrowed but are a bit more expensive; the upgrade for Roaches is worth it.
Creep Spread
Use your Queens' Spawn Creep Tumor to spread creep all over the map. Not just useful for letting you place buildings and increasing your units' movement speed, it also gives you vision wherever it reaches. Creep tumors are free, requiring only energy, so use them to spread your creep across the map. Creep tumors are invisible, so they can't be destroyed unless your enemy has detection. If they're destroyed, you can simply put more down when your enemy has been pushed back.