This is my first post and probably only post, so I'll try to make it count. I'm about to quit sc2 due to foreseeing a very busy schedule in the next few months. But I'd like to share my basic zvt strategy since a lot of zergs are having trouble with the ZvT matchup.
I'm about a 600 level diamond zerg, and ZvT is my best matchup by far, and I win most of my ZvT games against opponents anywhere from the 400s to the 800s in diamond. (If they get above 800, then they become beyond my skill level and it's just I'm too noob to do anything to win). My ZvP and ZvZ, however, aren't that good and that's keeping me back.
My basic strategy is early game to defend until I get mutalisks. Speedling with first 100 gas, then start teching to muta. After I get muta I start upgrading muta non-stop and commit fully to muta. I find that that's actually enough to win me a lot of my ZvT games. Go in his base and harrass with your muta, and try to pick off lone thors obviously. Meanwhile take a couple extra expos while ur opponent is holed up in his base (the key is start mining gas first!). Eventually, when he pushes out with like 4 thors, you should have 4 bases mining and at least 20-ish muta. That should be able to take care of his army. I like to mix ling/baneling in there for any bio units that come along with the thors. If he moves out with anything less than 5 thors, you should be able to just roll over him with your 20 something muta. I had a game where b/c of that early harrass, by the time a 6-thor (plus tank and hellions) push came out I had 23 muta upgraded 1-1, and completely destroyed his push while having 10 muta left over. And we all know that zergs can pump out a lot more muta much faster than terrans can pump out thors if you've kept him to 2 base. One extra benefit is that mass mutas really do pretty well against any variation the terran can throw at you midgame, like mass vikings or mass banshees that I see frequently in ladder games at this level.
I do dislike roach/hydra/speedling builds, because those depend so much on timing and you're at the mercy of your opponent in terms of when he wants to push and where the attack happens. With mass muta, you have control most of the game and can actually abuse the mobility that zergs are known for.
Obviously as I'm only a 600 level zerg I'm not that good a player, but as I'm winning a big majority of my games against equally skilled or slightly better terrans I feel I should should share this with other zergs having problems with the matchup. Even the games I lose, I feel that it's because I screwed up somewhere or the opponent had a really nice play rather than a problem with the build or any race imbalance issues. Hopefully the better zergs can actually improve upon this build and do some serious damage with it. Let me know if you do :p
Here are a couple replays that demonstrate this relatively well. I have a bunch more reps but I'm not gonna upload them all.
edit 4: http://www.mediafire.com/?p2xz052gm60903a <---- ~950 terran
edit: more replays:
Replays of how other types of aggressive terran play are dealt with here: