What are the popular build orders for Protoss in StarCraft 2?

I'm not sure if you mean openings or builds, but I'll give you both.

For openings, most Protoss start 13 Gate (9 probes, a pylon, 4 more probes, then a gateway). From here they will usually either build another Gateway or a Cybernetics core. You can go 10 Gate into a 2 Gate rush, but its less common.

There are a number of builds which go down these two routes:

• 1 Gate Expand
• 3 Gate Pressure into Expand
• 2 Gate Rush
• 4 Gate
• 3 Gate into Robo
• Tech into Starport

Since Protoss revolve around gateway units, its common to refer to Protoss strategies by the number of Gateways you build. Its worth noting, that with the exception of 2 gate, all Gateway based builds involve turning your Gateways into Warpgates (Learned at the Cybernetics Facility).

1 Gate Expand is a newer build that has caught on recently (1.1-1.2) with the advent of slower Terran Harassment (specifically Reapers) and more Macro oriented Zerg players. By scouting early and possibly delaying the first Gateway (to 14-ish) the Protoss player can create a much better economy and move to an early expansion. This early expansion allows for much faster gas production and a quicker move to powerful units like Colossus and Void Ray. Though there is an inherent risk in this sort of strategy a very early scout (eg. 8-10) can help make the decision whether to expand after 1 Gate or move to a more solid 3 Gate Pressure build. Liquid`Huk and TSL_GuineaPig are good people to watch for this build.

2 Gate Rush usually involves walling off your Main or your Natural with your first two Gateways and building 5-7 Zealots to rush with. This helps as a defense against any counter rush. This early rush style will later rely on using Warpgate technology to warp in units past that wall. This early rush banks heavily on Zealot's superiority to small numbers of other tier 1 units. This is most effective vs Fast Expand strategies. It also allows for an earlier expansion if you block off your natural.

3 Gate Pressure can involve either an early Cybernetics Core (preferred) or out of a 2 Gate style build. Given the high build speed based around Chronoboost and Warpgates, this build relies on building a very nice tier 1.5 army composed of Zealots, Stalkers and Sentries. This is a very standard opening for most Protoss players as it builds a very powerful army right at the start of the midgame. Try to remember to build Sentries as they are key to this build and Chronoboost your Warpgate technology. The strange part about this build is that it's place in the meta game has shifted drastically. While originally a very aggressive build it has changed to a more macro oriented build allowing the Protoss to use pressure to gain room to expand. Instead of use 3 Gate as a stepping stone to 3 Gate Robo or 4 Gate, a 3 Gate Expand leads to a much stronger 5 Gate + Robo allowing for good mid-game timing attacks.

4 Gate is the natural extension of 3 Gate allowing for a more powerful mid game push (possibly as a follow up to an earlier 3 Gate that was sucessful). This is the logical alternative to 3 Gate into Robo as a Protoss base can support 4 Gateways of continuous production or 3 Gateways and a Robotics Facility. 4 Gate can then move to Robo with the extension of an expansion or move to Templar tech. Templar tech is useful for Terran Bio assisted by Ghosts as the Templar can "snipe" the Ghosts, where as Robo is more effective against Terran Bio or Zerg Hydra/Roach

3 Gate into Robo rose up as a response to early Roach pushes at the beginning of Beta. This usually involved building the first gateway and then immediately teching to Robo before adding on additional Gateways. This provided for the Immortal timing push, which was a strong force backed up by an Immortal. Since the Roach nerfs, and other changes, its more common to build the Gateways first and add on the Robo later as a tech to Colossus. The Colossus gives this strategy an advantage vs Terran Bio or Roach/Hydra Zerg builds. Its also worth noting that 3 Gate Robo gives you an very early Observer which is immensely beneficial.

Tech to Starport builds grew out of early Void Ray rushes. Since those strategies cannot be maintained, a more common move is to instead build Phoenix out of the Starport and use graviton beam to destroy high priced units. These builds usually involve getting a number of Phoenix early and then bringing them along for a 3 Gate timing push. The delayed push is bolstered by being able to remove enemy units from the board. This is especially effective vs Terran Mech. Recently Early Starport has come back into favor with GSL 3. A number of players have been going for early double Starport (especially in PvZ). In addition to the early Phoenix for harass, they've also been adding in Void Rays. Void Rays were traditionally only a strong unit once charged, however, in patch 1.1.2 the uncharged damage was buffed. As a result Void Rays became much stronger both early in engagements and once they had reached large numbers. This combined with many Zergs relying heavily on Roaches after their range buff (also 1.1.2) lead to many more Starport centric builds.

Finally, it is worth noting there are a number of cheese builds. These revolve around hiding a Dark Templar shrine or Starport for Void Ray. While they are not sustainable builds, they are worth mentioning.

Note I use the terms:

Tier 1 to indicate: Zerglings, Zealots, and Marines.

Tier 1.5 to indicate: Stalkers, Sentries, Roaches, Banelings, Marauders, and Reapers.

In addition to Tzenes' excellent answer, you might want to check out this wiki; there you have:

• 1 Gate Core
• 10/10 Gate (vs. Protoss)
• 2 Base Robo (vs. Zerg)
• 2 Gate in base (vs. Protoss)
• 2-Base Zealot/Templar
• 4 Gate Push
• 4 Warpgate Rush
• Immortal Rush (vs. Zerg)
• Korean 4 Warpgate All In (vs. Protoss)
• One Base Colossus (vs. Terran)
• Photon Cannon rush
• Wall-In at Natural

And a general strategy for Protoss' build orders

1 Gate Fast Expand vs. Terran is more and more popular lately (according to TeamLiquid.net) I have had amazing success rate with it in gold/platinum

But seriously if you are looking for SC2 Builds: goto liquipedia

http://wiki.teamliquid.net/