My ZvT strategy of choice is zergling/infestor into crackling/infestor/ultra. I first learned about it through Mrbitter's stream and TL post in Jan/Feb. Stephano recently used it to great effect in his IPL win.
The rough B/O goes to the tune of: Early expand, take one gas, spend first 100 gas on ling speed, spend 2nd 100 gas on lair, take second gas and throw down two extractors. Upgrade melee and carapace. When lair finishes take remaining gas and put down an infestation pit. Research pathogen glands. Keep upgrading lings, get a third and a macro hatch, tech to hive, and start banking gas for +3/+3 and adrenal glands. Also put down ultra cavern and upgrade chitanous plating. Mass ultra and crackling. Use mobility to flank and try to deny terran map control. The rest of the game is an expansion war with fully upgraded armies. Don't forget to inject!
Theory: Zerglings are very mobile and keep map control until siege tanks and marine balls are out. I want the minimum amount of lings necessary to maximize drone production. Ideally I want three saturated bases with a fourth ready to accept drones from my depleted main. 70 drones is my goal.
*This strategy is economic and tech-heavy, so it is weak to early rushes in the form I gave above.
*A terran midgame attack with tanks and marines (9 minutes and above) will be met with infestors and lings. Infestors can fugal marines, volley infested terrans on top of tanks (or in marine balls to induce splash damage from siege). My upgrades should be superior and, so long as my injects are timely, I will have enough larva to reinforce an attack on my front.
*In a late-game scenario I need to be abusing my mobility and attacking weak points of the terran base.
*I should never attack a terran siege-line head on unless they have no more bases and I can instantly remax.
*Ultras tank and lings dps
Deviations
*First and foremost, I want the least amount of units possible, but until I've practiced against a strategy enough times I feel it's best to overdefend and not outright lose the game. Overdefense also leaves a bunch of leftover forces that can counterattack AND a great defense so I can make up for lost droning time.
*Hellion opening requires a spine, defensive evo's, and extra queen, and a few extra lings
*More than 6 Hellions, or BFH, require roach warren and a few roaches. Constant scouting will reveal these intentions
*Banshees and cloaked banshees require extra queens (4-5 total since energy is usually too low for transfuse) and a couple spores at each base
*1/1/1 needs extra queens and a lot of lings to defend banshee attacks/hellion drops/marine rushes simultaneously
*Beware of 9 minute marine tank timing attack. This is more of an anti-mutalisk attack, so be sure to make nothing but zerglings when I see this moving out.
*1 base marine/tank all-ins require three spines at the front (extended by creep tumors). These spines will keep terran busy while more forces hatch. 40-50 1/1 lings will dominate this all-in. Deny terran expansion and drone up like crazy once defended.
*Mech play should be scouted. Reaction is to expand to a quick fourth and have a roach-heavy army with broodlords on the way. This is the only strategy that requires a total change of strategy Ling/infestor is better-suited for a bio-heavy army. This change isn't very different from BW where pros went three-hatch muta versus terran bio/tank and mass hydra versus tank/goliath/valkyrie/vulture.
*Marauders suck against zerglings and I only ever see them in bizarre 1-base all-ins. Zergling numbers will compensate for concussive shells and, since marauders cannot mass as easily as reactor'd marines, I could have a few infestors out to bolster the defense.
rops are very effective since I have little air control. Leave a small pack of lings at each base and have ovies positioned to identify drops.
Good things to know:
*I have the more mobile army. If the terran army is defending the third I can send about 16 lings into the natural and kill scv's. Actions like this will either delay the terran army or send them into all-in mode. Expand or make a ton of units accordingly, but never sacrifice a huge army since it's not cost-effective.
*Constant scouting will show how much they expand. Early third bases almost always means more scv's and less units (so drone up and expand myself).
*Vikings will deny overlord spread, so if opponent sends them out make a spore and spine at each base and retreat overlords to safety.
*4 burrowed infestors with full energy can cough up enough infested terrans to take out a planetary. It's also fun to cause tank splash damage to other tanks, marines, or scv's by dropping one of these nearby. Sometimes chain fungals on an scv line is better than infested terrans since the scv's have a chance to run away from beach balls before they hatch.
*When one of my bases is under attack it is best to protect the drones. Running them away or using burrow is the best. It's a lot easier to recover the economic loss when only the hatchery needs replacing.
*Most terran expansions are built elsewhere and floated to the location. Have a ling on hold position, overlord dumping creep, a burrowed ling, or all of the above to delay the expansion and act as an indicator. Ovies should be at every expansion by the late game unless cleared out by marines or vikings.
This is by no means complete, but it shows you how much thought is involved in each step of the game. All the deviations I mentioned were from personal experience.