There is an unused fourth faction labeled "Independent".

Whether or not this faction was intended for play or was to be used exclusively in the campaign is unclear.
Contributed by Psychospacecow
In the retail release of the game, Zerg Devourers use the same cocoon as Guardians, but Devourers have their own cocoon graphics that go unused.
Contributed by Psychospacecow
There are three unused missions in game's retail release.
Spoiler:
•Biting The Bullet
A mission which would explain Tassadar's cooperation with Jim Raynor.
•Silent Scream
A mission where-in the player defeats the Confederacy.

•protoss/tutorial
An unused tutorial mission which would have featured a race called the Tagal.
Contributed by Psychospacecow
There is an unused critter designated for the space platform tileset, simply called "space critter". During development it was originally called the V'ger, which is a reference to the entity of the same name from Star Trek: The Motion Picture.
Contributed by Psychospacecow
Samir Duran's beret is the same color and shares the same insignia as the South Vietnamese Paratroopers during the Vietnam War.
Contributed by Psychospacecow
In the Nintendo 64 release, to access the free minerals/gas cheat, the player must "hug" an ursadon with their units.
Contributed by Psychospacecow
During development, the Rhynadon was referred to as "wasteland critter".
Contributed by Psychospacecow
The Nintendo 64 version of Starcraft has a slightly different story, different tutorials, and a bonus mission called Resurrection IV.

It also features several command buttons that did not exist in the PC version.
Contributed by Psychospacecow
The Ragnasaur critter was originally named "spots", and was found in the wasteland tileset. By the final release, they were given their present name of Ragnasaur and put in the ashworld tileset.
Contributed by Psychospacecow
The Kakaru critter resembles a prehistoric pterosaur, and appears to have been named after the kakuru, a cretaceous theoropod.
Contributed by Psychospacecow
The Terran Medic from the Brood War expansion-pack will say a couple of quotes from the Star Trek series. The first one is "State the nature of your medical emergency", referencing the EMH Program's opening line upon activation, predominantly in Star Trek: Voyager and a few times in Star Trek: Deep Space Nine. The second one is heard by continuously clicking on the Terran Medic until she finally says "He's Dead, Jim", which is an infamous quote said by Dr. Leonard "Bones" McCoy from Star Trek: The Original Series.
Contributed by G-Haven
Attachment
Waiting at the briefing screen for the 1st Terran training mission for about 3 minutes after the text ends will trigger a recipe for Chinese Lemon Chicken to scroll on the screen.
Contributed by KidDivinegon