Overview
The Protoss against Zerg encounters are a literal example of quality over quantity. The Zerg, with their cheaper units, 2 for 1 deals and 3 simultaneous unit production at each Hatchery, can produce massive numbers of units. The Protoss cannot hope to match them unit for unit, however, their superior technology gives them an edge in terms of raw power per unit. The key to defeating the Zerg with Protoss lies in meticulous unit micromanagement, quick expansions (you'll need the resources to produce enough of everything) and making sure every unit lives as long as possible (with the use of Shield Batteries).

Zealot Rush vs. Zergling Rush
The Zerg have the fastest rush in the game and depending on the map being played, you may find yourself being overwhelmed before your first Zealot is produced. By the time a rush like that hits, you should at least have one Pylon and a Gateway up with a Zealot beginning production, and in that case gather up all your Probes and lead the Zerglings on a chase around and around until your Zealot is produced. At that point, use the Zealot to attack and use your Probes to help it finish off the offending Zerglings. Once the Zerglings are dead, you'll want to recommence with your resource production as soon as possible. Note that a rush like this, this early in the game will severely hamper a Zerg player's resource production and the key to winning lies in making sure that you can out-resource and out-produce your opponent. At most they will be able to send another wave or two of Zerglings but by that time you should have a few Zealots out and able to defend without too many problems.

Getting Photon Cannons can help you out immensely in the early game against Zerglings and if you feel that your foe means to press the advantage of a Zergling Rush, you'll want to get them as soon as possible to help support your Zealots. Shield Batteries can also be extremely useful when defending.

If your opponent fails to pull off a Zergling Rush before you get your first Zealot, you shouldn't have too much to worry about in the early game. One Zealot can take 2-3 Zerglings by itself and once you begin Zealot production you should be ok. The only situation to watch out for in Zealot vs. Zergling encounters is overwhelming Zerglings numbers (more than 5:1 ratio of Zerglings to Zealots). This can easily happen if your Zerg foe builds multiple Hatcheries and builds only Zerglings and in such cases, you'll need to block up choke points with Zealots and Pylons and be well supported by Photon Cannons to fend off such numbers.

When using a Zealot Rush to invade a Zerg base, take caution and keep an eye out for Sunken Colonies. The Zerg can produce Sunken Colonies as fast as Zerglings and only a few coupled with a few Zerglings can really damage a Zealot force.

Hydralisks
Once the initial rushing is over, you can expect to face Hydralisks throughout the rest of the game. Hydralisks are relatively cheap and can also be produced in large numbers and they have a wide range of upgrades making them one of the most feared Zerg units, and rightly so. To counter them, you'll need Zealots to tie them up while you use Dragoons, Reavers or High Templar to finish them off. Reavers and Psionic Storm are your best bets against packs of Hydralisks and with a few good shots of either, you can raze a Hydralisk force in no time. Archons can also cause major damage to Hydralisks with their heavy hitting splash damage attacks. You can also use a Corsair's Disruption Web during a conflict to temporarily disable groups of Hydralisks.

Handling Royal Pains
The Zerg Queen, if used well, can become a rather nasty thorn in the side for a Protoss force. With their Spawn Broodling ability eliminating your High Templar, Parasites to see what's happening at your bases and Ensnare to slow and reveal your forces, Queens should be hunted down on sight. Corsairs and Scouts are well suited for the task since they are faster than the Queen and relatively cheap. With a pack of 3 or more Corsairs or Scouts, you should be able to make every base a Queen-free area.

Speaking of hunting, you should also make it habit to go Overlord hunting on a regular basis. The Overlord is even easier to pick off than the Queen and by killing stray Overlords (or even better, a stray pack of Overlords trying to hide in some corner of the map) you can slow down the Zerg unit production as well as decrease their chances of seeing or detecting any of your troop movements.

Mutalisks
The Mutalisk is the most mobile Zerg unit and flying in packs, they can quickly find and eliminate your forces or expansions. Their "ricochet" attack also causes substantial damage to packed units or buildings when they're in large groups and can be quite intimidating. But don't worry, the Protoss have more than enough in their arsenal to take care of this problem.

The first and best counter for Mutalisks is the Psionic Storm. Mutalisks will die beneath a Psionic Storm if they are left there for the entire duration of the effect even if they are at full health prior to the Storm. Also since Mutalisks stack on top of each other when grouped, making it even easier for you to destroy massive numbers of Mutalisks with a single use of Psionic Storm. But in most circumstances you cannot count on an opponent leaving their entire Mutalisk force in a Psionic Storm and they will usually escape with some of their health intact, so be sure to have support units nearby to quickly finish them off as they retreat.

In addition to the Psionic Storm, the Protoss Corsair is a countermeasure that was specifically built to engage the Mutalisk. Their quick hitting splash damage Neutron Flare attack can dissipate hordes of Mutalisks with little effort and they are just as, if not more, mobile than Mutalisks so they can hunt down Mutalisks forces no matter where they go. For even better results, keep your Corsairs slightly separated when attacking to reduce the effect of the Mutalisk attack.

Archons in groups are also deadly against Mutalisks. Their immense Plasma Shields protect them well from the Mutalisk attack and their splash damage attacks can kill Mutalisks in droves. However, if you do use Archons, be sure to have a few before engaging Mutalisks with them. A single Archon although powerful, cannot hope to prevail against a legion of Mutalisks.

Guardians
The Zerg are usually fond of using Guardians to eliminate ground forces of any species and with their attack range and power, they have a good reason to. However, they have a few weaknesses you can exploit with your own units. For one, they cannot attack other aerial units, making it easy to force them to retreat with a few Corsairs, Scouts or Carriers. Also Psionic Storm can be cast over them outside of their attack range and with their slow movement, they usually fall prey to a well placed Psionic Storm. Even if you don't have either means of driving off a Guardian force, you can always use Shuttles to load your more powerful units (Reavers, High Templar) to safety before the Guardians can finish them off.