Personally I don't open the same way versus every race, I use one build for each race and try to get each one perfect for that play-style so I can execute it well enough to beat anyone.
For ZvZ I use a gasless pool first opener:
9 Overlord
15 Pool
16 Hatch
15 Overlord
15 Queen
17 Zergling (for scouting)
22 Queen
24 2x Overlord
3/4th Queens Asap
37 Spine Crawler (if you scouted potential agression)
44 2x Gas
44 Roach Warren & Double Evo
Source:
https://www.youtube.com/watch?v=vIWR4ZPNOyQ (the rest of the build can be found here)
This build gives you a better economy and is incredibly good for timings and/or going into longer macro games.
The current meta of ZvZ generally revolves around a lot of roaches with transitions into hyrdalisks/infestors in the mid-late game, longer mutalisk styles are becoming less common because of spore crawlers hard countering them so much, generally if a person opens mutalisks, you'll often see a transition into double evo roach warren while they use mutalisks to get as much damage done as possible.
For ZvT I use the following:
9 Overlord
15 Hatchery
16 Spawning Pool
17 Overlord
19 @100% Spawning Pool, start 2 Queens and 2 Zerglings
24 Overlord
30 @100% Queens, start 2 more Queens
36 2 Extractors
@100% Extractors, start 3rd Hatchery
@100 Gas, start Metabolic Boost, and 2 Evolution Chambers
@100% Evolution Chambers, start +1 Melee and +1 Carapace
Source:
http://imbabuilds.com/hots-zerg/hots-zvt/zvt-scarletts-3-hatchery-macro-opener/)This build is scarlett's 3 hatch opener, it is a very good standard build against bio; however, this build can be used against mech, but adjustments should be made (ex: roaches instead of a baneling nest). The current ZvT meta generally has zerg securing 3 bases while Terran opens reapers with hellions and possibly banshees in order to get damage done early on. It is incredibly important to make sure that this force
DOES NOT GET DAMAGE DONE, afterwards going up to 4 bases and getting a good muta-ling-baneling army is the best way to go
A good continuation of this build is Scarlett's macro mutalisk style:
http://imbabuilds.com/hots-zerg/hots-zvt/zvt-scarletts-macro-mutalisk-style/ IF they are going bio.
For ZvP I generally do the following:
(In the early game
LOOK FOR CANNON RUSHES, keep your second overlord at the natural)
9 – Overlord
15 – Spawning Pool
15 – Hatchery
15 – Overlord
@100% Spawning Pool, start a Queen and 2 Zerglings
@100% Queen, start 3rd Hatchery and 2nd Queen
@1st Creep Tumor, start 3rd Queen
Benchmark: When you start your 3rd Queen (@5:15), you should have 2 Queens and around 25 Drones.
@100% 3rd Queen, start 2 Extractors
@100% Extractors, start Roach Warren
@100 Gas, start Lair and Evolution Chamber
@100 Gas, start Metabolic Boost and 3rd Extractor
@100 Gas, start +1 Missile Attack, Macro Hatchery, and 4th Extractor
@100% Lair, start Roach Speed
Benchmark: When you start Roach Speed (@8:45ish), you should have 3 Queens and around 60 Drones.
————–Above is HyuN’s 3 Hatchery Opener
@100% 3base saturation, start Infestation Pit, Hydralisk Den, and 5th/6th Extractors
3 base saturation = (16 DronesOnMinerals)*(3 Bases) + (3 DronesOnGas)*(5 Extractors) = 63 Drones
@100% Infestation Pit, start Hive and 4th Hatchery. Make Roaches to defend, use Spore Crawlers for anti-Phoenix for now. Aim to have at least 600 gas floating for Vipers after your Hive finishes, so keep this in mind whilst making Roaches.
@100% Hive, start 3 Vipers, 2 additional Spores to Consume for Viper energy, and 7th/8th Extractors.
@100% +1 Missile Attack, start +2 Missile Attack
@100% Hydralisk Den, start Hydralisk Speed
@100% Hydralisk Speed, max out on Roach/Hydra and start Grooved Spines
Attack your opponent’s 3rd when Grooved Spines finishes (@13:30) with a 200 supply army of Roach/Hydra and 3 Vipers and prepare to re-max on the hive-tech of your choice.
Source:
http://imbabuilds.com/hots-zerg/hots-zvp/zvp-hyuns-roach-hydra-viper-play/This is HyuN's roach/hydra/viper build, this build is centered around hitting with a strong mid-game army against colossus as this is the most current meta. Roach hydra beats just about any gateway army so long as the engagements are taken well (this includes the common path of getting 3 bases and moving out with +2 attack and blink), so getting rid of the colossus is a priority. However, if you see that your opponent is going for High Templar rather than colossus, then vipers should be delayed until you scout any sort of colossus transition (because feedbacks will render the vipers useless). This composition shouldn't be used for very long because it is not the most cost efficient and is extremely dependent on having a higher base count/economy than your opponent. Tech switching is the most common way of dealing with hard counters, make sure you are scouting for possible tech transitions and counter attacks (proxy pylons).
All of the scouting and timing details can be read in the links attached to each respective build.
Hope this helped!