Power Generator
After the arrival of the UED to Braxis, their scientists constructed the Power Generators necessary to activate the Psi Disruptor continuously. At the beginning of Episode 6, Kerrigan makes a deal with her Terran comrades, especially Arcturus Mengsk, to lead a contingent of Terran invaders of the Sons of Korhal to destroy the Power Generators, thereby enabling Kerrigan to control her minions, which then land on the planet. Subsequently, Kerrigan's Zerg brood destroys the Psi Disruptor so that UED power in the sector is crushed.
 Psi Disruptor
Although the Confederacy, when they were in dire trouble from the Zerg infestations, could not find their own Psi Disruptor, which was directed specifically against the aliens, the arrival of the UED resulted in this pivotal structure's resurfacing...on Braxis, a former Protoss colony. Through the rest of Episode 5, the UED Terrans use the Psi Disruptor--despite Duran's attempt to demolish it from within--to weaken the hold of both the Overmind Cocoon growing on Char and Kerrigan the Queen of Blades on their Zerg minions. This quickly led to the Overmind's capture and then drugging by the UED's Medic's Neurostims. Thereafter, the UED power in the sector consolidates.
 Ion Cannon
The Confederacy seems in favor of doing too many experiments; one of these falls into the hands of the Sons of Korhal as Raynor's Raiders splinter off from the terrorist organization. It makes a brief appearance in the last level of the Terran Episode 1, in which Raynor and his forces make a daring attack on the Ion Cannon and then flee from the Koprulu Sector.
The primary Zerg structure in its hierarchy is the Overmind, which according to lore was created by the Xel'Naga on Zerus but which subsequently moved to Char to direct its campaign against the Terrans. It is the greatest weak point in the Zerg race; if it dies, the war would be over. It DOES get killed by the Warp Blades of the Dark Templar, thus throwing the Zerg into disarray, but not before the Overmind had judiciously metamorphosed a Terran Ghost--Sarah Kerrigan--to act as replacement. In Brood War, then, this Queen of Blades takes control over most of the remaining Zerg.
The Overmind declares to a Cerebrate at the beginning of Episode 2 that his Covenant is resurrection. This becomes important in Episode 3, where this patronage of the Overmind leads to strife within the Protoss camps and leads to the search for the Dark Templar, who possess the energies (Warp Blades) that can permanently kill the Cerebrates.
Why so important? Each Cerebrate--there are at least ten--controls its own brood, each of which poses a significant challenge for any Protoss or Terran fleet. By destroying a single Cerebrate, the Dark Templar would throw the entire brood into disarray, and cause the Zerg to turn on themselves. The Cerebrates are directly under the Overmind, yet they cannot move, which makes them a very important target for enemy forces. The Cerebrates in turn directly control the Overlords, Queens, and possibly Defilers; those in turn control the rest of the Swarms.
Cerebrates are created by the Overmind, albeit at a slower pace than its minions; Episode 2 begins with the Overmind's first speech to its newly created Cerebrate (the player) and binding of the Cerebrate with Sarah Kerrigan, Queen of Blades and Queen of the Zerg.
Following the Xel'Naga's revealing themselves to the Protoss, there followed a period of peace, during which the Protoss created temples to worship their creators. They have the most basic technology--reminiscent of the ancient stone-construction civilizations--and the Protoss prize them greatly. Near the end of Episode 2, the Overmind considers crushing one such temple to devastate Protoss morale as an introductory assault against the Protoss homeworld.
 Khaydarin Crystal Formation
Lore says that the Protoss energies are connected to the Khaydarin Crystals, which are scattered throughout the galaxy. The Protoss keep their secrets carefully guarded, lest the Zerg gain control of them. The Protoss have one particularly large and significant formation on Aiur, but they have only begun to decode its existence. Meanwhile, the Overmind claims that its Zerg can do better in unlocking the secrets of the Protoss' own energy source. The newly created Cerebrate of Episode 2 leads an assault to capture a chunk of the Khaydarin Crystal near the end of the campaign.
What is it used for? StarCraft hints that chunks of the Khaydarin Crystals fuel the energies of the High Templar, or at least improve their energy stores. The Khaydarin Crystals may also be essential in boosting Protoss morale--as they are psionically attuned, and an excess of energy creates psychological warmth for them--and on a secret mission of BroodWar in which Duran says that he has begun a project to unite the Zerg and Protoss in the name of the Xel'Naga. Only the obtainment of the Khaydarin Crystals by the Zerg allows the Zerg to obtain the secrets of the Protoss enabling them to creat their Hybrids, which are likely to appear in StarCraft 2.
 Xel'Naga Temple
The Xel'Naga temple on Shakuras has a strange property: using the Uraj and Khalis crystals there can obliterate all Zerg on the planet. Subsequently, both the Protoss and the Zerg battle for control of the strategic temple, with the Protoss ultimately winning and scouring the planet of their perpetual foes. The story is told in Episode 4.