The Night Elf Banshee's portrait is a direct reference to the Night Elf race from Warcraft
Contributed by Psychospacecow
The Urubu's name is Portuguese for "vulture" or "buzzard".
Contributed by Psychospacecow
Nyon is never named in-game, and sub-titles refer to him as the "Tal'darim Executor.", the name "Nyon" was derived from various sources, such as his official portrait.
Contributed by Psychospacecow
Blizzard went through many different concepts for the hybrids. The unused designs were "aquatic and graceful", intended to convey a more advanced alien species than the Protoss and Zerg.
Contributed by Psychospacecow
The goliath's portrait is based on Dustin Browder, lead designer of Starcraft 2 and game director of Heroes of the Storm.
Contributed by Psychospacecow
The Protoss Immortal's portrait occasionally shows a goldfish, when asked about it, lead designer Dustin Browder jokingly said it was named "Herbie".
Contributed by Psychospacecow
New Folsom Prison is a reference to Folsom State Prison in California, one of the first maximum security prisons.
Folsom State Prison in most well know for the Johnny Cash song, "Folsom Prison Blues", which was also performed there in concert.
Contributed by Psychospacecow
Zeratul was originally planned to be the main focus of Legacy of the Void, but the developers felt that as Legacy of the Void was a protoss story, Artanis was in a better position to represent the Protoss race as a whole.
Contributed by Psychospacecow
Holding down the button for the FPS counter (Ctrl + Alt + F) for more than 10 seconds will cause a strange face to appear under the FPS counter.
Contributed by DrakeVagabond
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During development there was originally a Protoss ranged unit referred to as the "Soul Hunter" and then later as the "Purifier". It was canceled because of its heavy anti-zerg focus, and because it was hard to recognize in large battles.
Contributed by Psychospacecow
Dehaka's right arm can be found in the Supreme mission.
Contributed by Psychospacecow
In The Heart of the Swarm campaign, the character can overhear Abathur in the evolution pit say, "Must solve lemon juice allergy hinderance in zergling strain." This is a reference to a news feed in Wings of Liberty where Donny Vermillion ends the segment with some speculation: "Up next: Are zerglings allergic to lemon juice?"
Contributed by Psychospacecow
The mission "Welcome to the Jungle" in the Wings of Liberty campaign is named after a song by Guns N' Roses. The achievement "Appetite for Destruction" is named after their first album, and the achievements "It's So Easy" and "You're So Crazy" are also named after Guns N' Roses songs.
Contributed by Psychospacecow
In StarCraft 2: Wings of Liberty's third campaign mission, there is a Tauren Marine hidden on the map. Clicking on him three times starts a countdown which will cause him to lift off in a portable toilet.

He can then be seen flying through space from the bridge of The Hyperion and on certain missions.

Tauren are from the Warcraft series, also developed by Blizzard.
Contributed by Psychospacecow
Diablo, from the series of the same name, can be found on the bottom right corner of the map in the mission "Devil's Playground".
Contributed by Psychospacecow
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During the fourth mission "Harvest of Screams", in the Heart of The Swarm expansion, you can see a set of armor frozen into the side of a cliff. This is the Lich King's armor, a reference to the second expansion of World of Warcraft, "Wrath of the Lich King".
Contributed by cross307
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During the mission "Piercing the Shroud", you can find a Metroid from the Metroid series in one of the many containers in the background. These containers can't be interacted with, and are just decoration.
Contributed by cross307