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When compared to terrans and protoss, zerg don't have omnipotent units like battlecruisers or carriers. Most of the players then rally on swarming vast amounts of units, preferably hydralisks or mutalisks. Their late game additions are ultralisk, defiler, guardian and devourer, although limited, they are quite useful.
Zerg have an edge on dropping - all overlords you hatch are potential transporters. This makes it easy to make massive drops. But, just go and drop a player won't always bring you the so-much-wanted victory. Flanking must be included to do a devastating effect. Estimate your forces and send as much as needed to break one base's defenses. After this, if your attack gets attacked, drop! Not only your opponent will be busy defending expansions but, his army will be split. Doing a drop like this usualy wins you a game, but don't get carried on - your opponent just might do the same.
Compared to the marines push, zerglings are much less versatile units, but more powerfull. The preferable opening for the zergling push would be 3 hatcheries. Your initial attack should be with 12 zerglings, and any other with 24. Each attack, build 4-12 hydralisks for defense, depending on if your opponent is getting light or heavy air support. Your first upgrade should be the zergling speed, then, in two evolution chambers, attack and carpace, if you get to hive, get adrenal glands at once (faster zergling attack). If your opponent bunker up, don't worry, you'll have the map control and the game is yours to win.
Defiler has powerful spells. The first and "free" spell is the dark swarm, a very useful spell that prevents any ranged weapons firing in it. A very good cominations are zeglings/swarm and lurkers/swarm (lurker attack is not considered ranged). Second defiler spell is the plague, with a high cost of 150 energy, it is a killer spell against protoss and zerg, and somewhat terrans. It causes up to 300 damage to the units or building. but it doesn't kill it. If used against protoss, they will have no means of repairing the damage, zerg units heal quite slow and terrans can both repair and heal the affected units. The third spell is consume. Well, not really a spell itself, it gives a defiler ability to consume friendly units to gain more energy.
The infested terran is unit you can produce from the infected command center. It's power is obvious - it causes 500 explosive splash damage. To use it properly, however, it's not easy. Except for the self-destruction, infested terran has no other weapons, therefore it doesn't fire back. This is very usefull when attacking - say one ridge is fortified with a bunker and 2-3 tanks, it would be possibile to kill all of them with a single infested terran if they are close to each other and, of course, if the infested terran could reach the given position. A small attack with about 6 hydralisks would do nothing if it attacked the fortified ridge but 6 hydras with just one infested terran can kill it of completely. By sending the hydras initially they will draw the fire from the tanks and the bunker - none of them will fire on the infested terran because it doesn't fire back! Just watch it exploding and - voila, all that's left are the units in the bunker.