The Starcraft Command
Tip: Protect your Overlords. Not only can they detect cloaked units, but they are also "houses" of a sort, meaning that as you lose Overlords, the number of units you can evolve is reduced.
Tip: Burrowed Zergs still have visibility. It's a great way to keep your eye on certain parts of the map without sacrificing your units.
Tip: Burrow, burrow, burrow. If your drones are being attacked, don't let them get picked off like sitting ducks. Burrow them until the cavalry comes around. Just don't forget to unburrow them!
Tip: Defilers are excellent for slightly covert operations. Burrow them near your enemy's front line until they build up enough mana to cast Plague, which is capable of dropping a defensive building fast. As soon as you've cast Plague, immediately burrow your Defiler again. By the time your opponent looks to see what attacked him, you'll be out of sight, building up your mana again.
Tip: Use the Queen's Infest Terran Command Center ability against your enemy's expansion sites. Wait until one of your opponents expands and then infest his center for some good old-fashioned fun.
Tip: When staging your troops in preparation for an assault, burrow them. This is the equivalent of cloaking them. This doesn't guarantee that they won't be seen, but if your enemy is making a quick visual sweep or flyby, they probably won't notice just how many guys you're massing. This way, you won't tip your hand.
Tip: Learn to love Parasites. They last a really long, long time, and even if your enemy notices that you flew a Queen by, he'll usually have bigger fish to fry and won't worry about tracking down a parasited worker unit. An upgraded Queen with 200 mana can parasite four units from a nice, long range, and give you reconnaissance (plus some destruction) within your enemy's base. For best results, position yourself just barely in the range of your enemy's resource lines. When you see one peasant, parasite it. Once the shared vision kicks in, you will be able to target units farther away without getting any closer.
Tip: Spore Colonies have excellent range. Use them all along the town perimeter, and stack them inside your interior base as well. Zerg defensive structures take longer to build compared to the other races, so don't count on beefing up your defenses at the last minute. You have to think ahead. On island maps, Spore Colonies provide the best defensive line of any of the races.
Tip: Fully upgraded Hydralisks do well against air or ground units. Always keep a bunch at home for defensive purposes.
The Air Attack
Tip: Scourge delight. Use them against Carriers and Battlecruisers. You should always have eight or ten of these mini-fighters hot-keyed and waiting in reserve. When you get attacked by a superclass ship, grab your Scourge group and aim them directly at your target. A few will get picked off, but as long as five or six hit the target, you'll take it out.
Tip: The Queen. Don't underestimate the power of the Queen. She's high maintenance, but well worth the effort. Her Parasite and Broodling attacks are unstoppable.
Tip: Share the wealth. Early in a contest, you can use your Overlords for reconnaissance purposes. No one else will have anything that can kill them yet (except for Terran Marines). Send them out until you find a couple of enemy bases, then send them to your allies' camps so that they can see cloaked enemy units.
Tip: Take advantage of the fact that the Guardians out-range just about everything. You can't just leave Guardians on their own, because they're weak on defense and can't go air-to-air. But if they're defended by a group of Mutalisks, they can wreak some serious damage on defensive structures like Missile Towers. This combination will also be really effective against Protoss Zealots.
Research and Development
Tip: Because Zerg drones actually mutate into buildings, be careful not to let your resource-harvesting lines dwindle. Zerg worker units are cheap so you should be constantly cranking them out all through the game. You'll never waste them, because you can always use any extras for building creep colonies.
Tip: By midgame, you should be cranking out three Overlords at a time--well before you actually need them. Because they cost only 100 minerals, this is relatively easy. By evolving lots of Overlords, when you lose a few in an attack you won't be crippled too much.
Tip: The Nydus Canal is your friend. As soon as you've set up a second base location, build a Canal ASAP. With it, you'll be able to mobilize troops fast.
Tip: You can also use the Nydus Canal to spring an attack on your enemy. If you can get near an enemy encampment, and then place a Hatchery close by, you'll be able to place a Nydus Canal within striking range of your opponent's base. And we don't have to tell you what that means...
Tip: Once you've completed the increased sight and speed upgrades for your Overlords, keep one or two of them attached to your advancing lines of Mutalisks/Guardians. This is especially important against the Terrans, with their godforsaken cloaked Wraiths.
Tip: Because the Zerg units all come from the Hatchery, you can only choose one rally point for all your guys. You should still set one, though, as your Hatchery usually ends up being a traffic jam of drones, worms, and units (if you're doing it right). Set a rally point just a couple of inches away from the Hatchery, so that you can easily pick out the new units as they hatch.
Tip: By mid- to late game, don't be afraid to plop down a Hatchery near your allies or team staging area (usually the center), even if it's not near resources. This will give you another troop factory; even better, it will let you build a Nydus Canal from your most defended area to your allies' bases, or to the front lines. It doesn't cost anything. At worst, it's a decoy that your enemies will waste time attacking.
Tip: On a map without lots of gas, shift to a low-gas economy and use what gas you can get your hands on to upgrade your Hydralisks as much as possible. A group of 40 fully upgraded Hydralisks can rip just about anything to shreds.