Here are some of the more common early to mid-game “all-in” pushes for protoss:

Warp Gate Rush
Hide a pylon near, or inside, the enemy base while you use chrono boost to speed up warp gate research until it is completed. Build three or four gateways during the process, and make sure construction finishes by the time research is done. Switch the gateways into warp gates and begin warping in units at your proxy pylon. Once you feel you have enough units (scout your enemy beforehand) attack. Remember to continue reinforcing your push, and chrono boost your warp gates as needed. [Learn more]

Counter: Scout aggressively, especially if you see your opponent spending chrono boost on the cybernetics core. If you find a proxy pylon, destroy it immediately. This will set back the push to a point where it becomes significantly weaker. Using force fields to block your ramp until you can get an immortal will also help you survive the push. Zerg and terran players can prepare for the onslaught by incorporating static defenses like bunkers or spine crawlers.

Dark Templar Rush
The dark templar rush is a strategy that capitalizes on speed and the element of surprise to gain you the upper hand in the match. As such, make sure to keep your intentions well hidden from your opponent's eyes.

Begin by building a pylon and a gateway, then follow up with an assimilator, another pylon and a cybernetics core. After that, construct another assimilator and begin saving chrono boost to speed up warp gate research later on. Get the remaining structures you need to begin producing dark templars: twilight council, and dark shrine (be sure to hide it well); add two more gateways and begin warp gate research when all the infrastructure is ready. Don't forget to build a proxy pylon near the opponent's base for quick assaults (though you'll probably have to walk your first batch of dark templars there). Ideally, you will be saving all of your vespene gas to produce dark templars, and only have a few zealots on your ramp for defense. However, depending on what the opponent does, you might need to add a couple stalkers or sentries to the mix (not recommended because they are gas heavy, but it's a better alternative to losing, or allowing your opponent to spot your dark shrine and becoming savvy of your plans).

When attacking the enemy, be sure to micromanage your dark templars. Anything that will slow down your opponent's economy or production is a good target. For example: workers, tech structures, supply structures, larvae, queens, M.U.L.E.s, among others. Keep an eye out for detectors and happy hunting.

Counter: Scout aggressively and thoroughly. If the enemy hasn't expanded and you don't see many sentries or stalkers (or conversely a large army), he may be going for dark templars or air units. Look for proxy pylons, place detectors and defensive structures by your mineral line, and get mobile detection as soon as possible.

A protoss player sends over a warp prism and converts it to phase mode.	The protoss player begins warping in dark templars and other units right outside the enemy base.
Two dark templar strike at an enemy base.	A protoss player keeps the dark shrine hidden so the opponent won't know about the dark templars until it's too late. Smart.
Two dark templars scare off a terran army.

Void Ray All-In
This build aims to catch an opponent off-guard to end the game quickly, or cause enough damage to his economy that he won't be able to recover. 

Construct a pylon and a gateway, then an assimilator, another pylon and a cybernetics core. Use chrono boost on your nexus, but save two casts of it to speed up warp gate research as soon as the core is finalized. Build a stalker, or a few zealots, and two stargates (you can add more stargates/gateways as your resource income allows). Make sure your stargates are well hidden (you can also build them close to the enemy base, but this is risky).

If you wish to attack early, send in your small ground force through the front of the enemy base as a distraction and 2 void rays to harass the mineral line (focus fire those workers). If not, build up your fleet a bit more. Try to keep the void rays charged all the time and micromanage them to prevent losses. Eventually you'll have a large force that will be pretty difficult to stop; especially if you were successful in damaging your opponent's economy. Keep your eyes peeled for changing battlefield conditions, however, and don't forget to expand and change your game a bit if your opponent manages to repel your attack.

Counter: Apply the golden rule, scouting, scouting, scouting. If you notice your opponent going for air superiority, get anti-air defenses as soon as possible. For terran players, marines provide a solid counter, just be careful not to engage near cliffs, as void rays have a longer attack range. Vikings are also effective, but to make the most out of their long range missiles, you'll need to kite the void rays around. Zerg players can use hydralisks, spore crawlers and queens, while protoss players can warp-in stalkers or use high templars to cast psionic storms (void rays tend to bunch up). [Learn more]

Blink Stalker Rush
Stalkers are a well rounded unit that can be outfitted with the ability to Blink, which is a short distance teleportation. Blink allows stalkers to circumvent enemy defenses and terrain obstacles (provided you have vision of the high ground you wish to blink to), as well as retreat when things are not going so well. With a sizable amount of stalkers and an observer to spot for you, you can blink onto the enemy's main base and wreak all sorts of havoc. Additionally, you can blink damaged stalkers to your rear line to prevent them from being destroyed by the enemy (the units targeting that stalker will pick the closest target to continue attacking).

Counter: Immortals and colossus-based armies are the most effective counters to stalkers with blink, but you might have to do something to force them to engage your troops (like attacking an expansion or main base). Zerg players should spawn large numbers of zerglings and use the infestor's fungal growth to prevent damaged stalkers from blinking to safety. Terran players are best served with large numbers of marauders with stimpacks, as marauders have a nice damage bonus against armored units. All three races should keep an eye out for cloaked observers, as their field of vision is more than likely helping the stalkers to blink onto higher ground.

Some stalkers fire at the assimilators across the ravine. They can blink back, forth, up, and down the nearby high ground as long as they have vision.