StarFox (known as Star Wing in the UK) was developed by Argonaut (of later Vortex infamy) and published in the US for the SNES by Nintendo on February 21, 1993, after critical delays that prevented it from being released in time for the holiday season. The game (as of this noding) is fairly easily acquired anywhere that used SNES games are sold. The ROM is readily available and complete; just make sure your emulator of choice has good SuperFX emulation. (Most do.)
While the game draws greatly from previous 3-D games using vectors or stretched sprites, StarFox was quite possibly the first console game to use 3-D graphics constructed of polygons (Out of This World predates it for polygon use in a console game), with the help of the processing power of the SuperFX chip, first used in this game. While the graphics are painfully dated by modern standards, the game was a revolution at the time, as other "3-D" console games at the time generally used stretched/shrunk sprites and bitmaps mapped onto a flat "ground" surface.
The story is right out of the Big Book of Video Game Cliches. The peaceful planet of Corneria has been attacked by the space fleet of the evil Andross, with the feeble defenses of the pacifistic planet swept away. Fox McCloud and StarFox pilot team (composed of Falco Lombardi, Slippy Toad, and Peppy Hare, commanded by General Pepper) take to the skies in Arwings, experimental space fighters, and go off to defeat Andross (a mad scientist banished from Corneria, now bent on controlling the galaxy) or die trying.
After choosing from one of three different paths (Easy, Medium, and Hard, each with a different set of stages), the player takes control of Fox McCloud, the protagonist, and his Arwing, and begins the long, hard path to defeat Andross, starting on Corneria, travelling through nebulae and asteroid fields and over different planets, all on the way to Venom, Andross's home base. The stages themselves follow a strict, straight path, with no reversing or veering off to the left or right.
While most of the stages are space-shooter staples (Sector X and Sector Y have lots of drifting geometric shapes, even), some of the stages are especially imaginative, given the limitations of the graphics. Titania, for example, has all sorts of interesting (and deadly) flora and fauna in place of the more convential enemies, as well as a giant hydra for the boss.. Generally, the most challenging parts return to the shooter convention of "Fill the screen with flying nastiness", usually composed of storms of laser fire, squadrons of suicidal enemy fighters, or barrages of surface-to-air missiles .At the end of each stage is some kind of massive boss, which, generally, has one weak spot that you shoot until part of it falls off, after which you need to shoot a new weak spot. For some reason, you seem to fly infinately forward, as bosses always have all the room they need.
While Argonaut wasn't involved, there was a StarFox 2 in development (but scrapped), and a StarFox 64 for the N64. As of this noding, StarFox Adventures: Dinosaur Planet has been released on the Gamecube, and has a dash of StarFox-style space combat added to a great deal of Zelda 64-style adventure.
StarFox: Competition Weekend Version ||
StarFox 2 || StarFox 64 || StarFox Adventures: Dinosaur Planet
Sources: GameFAQs, MobyGames, and a heaping helping of correction and advice from MightyMooQuack and jpfed.