"Eye of the Storm", the final mission of the Protoss campaign in the original StarCraft. Raynor and his surviving Terran troops teaming up with Tassadar and his surviving Protoss to come together to try and defeat the Overmind. Controlling two races, each on opposite sides of the map made it really feel like a great moment. Not to mention the aftermath and Tassadar's crowning moment of awesome.
"Emperor's Flight". You as the UED start off by using a fleet of Valkyries and Siege Tanks to wipe out a Zerg base and claim it as your own, so you can assault a Protoss base before your targets escape to a warp gate (said targets are Terrans hiding out in a conspicuous Command Center in the base). Then as you begin building up your forces, you get a message that the warp gate has activated and its energy is inciting passive Zerg in the area to attack. From there you fight a three-pronged war, Terran, Zerg, and Protoss, all mixing it up. Then when you win, a third Zerg force operating for an unknown fourth party attacks you and the Protoss so the Terrans can escape. The mission is practically a microcosm of what Starcraft is all about.
"To Chain the Beast", the final Terran mission, has you turtle up for the majority of the mission penned in by invulnerable Combat Tentacles and a semi-unkillablesuper-Ultralisk. Fortunately, the three Keystone Armies are quite vulnerable to a few well-placed Yamato shots, after which you can disband all your defenses and send them on the (second) biggest turkey shoot in the galaxy.
Raynor:Well, I guess all I have left is to see this through. The Zerg have taken everything from me. My home, my friends, my family. I know that nothing I can do can bring those things back but I'll be damned if I just sit on my hands and wait for the end. I want a piece of them all right. I'm in.
Don't forget this precious piece of dialogue from Brood Wars.
Fenix: It is difficult to believe that I am working along side my greatest enemy in order to save this sector.... Fortune has been whimsical of late.
Raynor: You sound like a tired old man, Fenix!
Fenix: Don't let the fact that I am 368 years older than you dull your impression of me young Raynor, I can still - how do you Terrans say it? - 'Throw down with the best of them!'
Raynor: I stand corrected.
Raynor talking back to the Protoss for mocking him.
Tassadar: Arrest me? Aiur burns at the touch of the Zerg, and you come all the way out here to arrest me?!
Kerrigan gets another one when she mocks Fenix by quotingTassadar's "you are your own worst enemy" at him. Despite Fenix immediately lampshading the irony, the fact that she can do this with a perfectly straight face really shows how far she had come from the near-Blood Knight she started out as after she was zergified.
Kerrigan does it again at the culmination of Brood War. She seemingly invokes Enemy Mine by rallying Raynor, Mengsk and the Protoss against the UED - but as soon as Korhal is retaken and Mengsk is restored to power, she turns around and backstabs all parties involved when they least expect it, ensuring that Mengsk can't pose a threat to her and eliminating one of the two high-ranking Protoss leaders left after Aiur's fall. Next, she blackmails Zeratul into restoring her to undisputed power over the zerg then forces him to do something she knows will make his life, in her own words, "a walking torture day by day". And when she gets cornered by three separate factions rightly pissed at her, she counterattacks and sends two running home to lick their wounds as well as completely wiping out the UED. The same UED that pretty much came, saw and systematically kicked the crap out of every single faction in the Koprulu sector in one go. And she wiped them out - not defeated, killed down to the last man.