The series focuses on the humanoid fox, Fox McCloud, and his efforts to stop the evil scientist Andross from taking over the Lylat System. Unlike quite a few other Nintendo franchises, the Star Fox series actually tries to tell a coherent story and to maintain continuity. So far, the only game in the series that has proven impossible to fit into the storyline is the original SNES game. However this is because Star Fox 64 for the Nintendo 64 was a remake of the game, and thus it replaces the original storyline rather than being a sequel to it.
In the Super Nintendo game and original comics that ran in the official Nintendo magazine issues 45 through 55, Nintendo Power, which are both in the original continuity, Fox receives a distress signal from Director-General Pepper to come to the Lylat System's aid. Immediately setting off for Pepper's homeplanet of Corneria via stowing away on a starship, Fox and his team members- Slippy Toad, Peppy Hare, and Falco Lombardi arrive on Corneria just as the forward attack force of Andross's armada of ships arrive.
Quickly Team Star Fox jumps into the cockpits of the prototype super-advanced starfighter, Arwing, which Pepper believes to be the only ship capable of defeating Andross. They graduate from basic training quickly and before they can rest they're dispatched to protect the city they're in from attack. Pepper's prediction is right- after many, many battles with various enemy starships Fox reaches Venom, first planet of the Lylat system, and fights his way to Andross's lair. It is there that he comes across a metallic silver face, one that Andross formed using his Telekinetic Amplifier in order to protect his central Core Brain from being destroyed.
Fox managed to shoot apart the apparition, though, and he laid waste to the core. Escaping from the self-destructing, base, he rejoins his team and they boost off back to Corneria as heroes. Andross still lives...
Star Fox 64
In the Nintendo 64 game and official adaptation of the game which ran in Nintendo Power, Star Fox 64 (or Lylat Wars in Europe) we are given a background to both team Star Fox and Andross's crusade against the Lylat System:
"Corneria, fourth planet of the Lylat System. The evil Andross turned this once thriving system into a wasteland of near extinction.
General Pepper of the Cornerian Army was successful in exiling this maniacal scientist to the barren, deserted planet Venom.
Five years later, General Pepper noticed strange activity coming from Venom. James McCloud, Pigma Dengar, and Peppy Hare of the Star Fox team were sent to investigate. Upon their arrival, Pigma betrayed the team, and James and Peppy were captured by Andross.
Peppy barely escaped Venom and returned home to tell James' son Fox about his father's fate.
A few years have passed. Andross has again invaded Lylat system. General Pepper has turned to a new Star Fox team headed by Fox McCloud to save Corneria and free the Lylat System once again."
The Star Fox team is patrolling the Lylat system in their mothership, the Great Fox, when Pepper appears via hologram, saying: "We need your help, Star Fox! Andross has declared war and is trying to take over Corneria! Our army alone can't do the job. Hurry, Star Fox!"
The team quickly scrambles their Arwing fighters from the Great Fox's hangar bay and speeds towards the planet, which is heavily under siege. Checking their G-Diffusers, they liberate Corneria and continue on their quest to save the Lylat System from Andross's reign. Along the way they encounter Star Wolf, a rival group of mercenaries led by the cunning Wolf O'Donnell. After a long battle above the planet of Fichina (and/or later a satellite, depending on in-game choices made by the player), Star Fox emerged victorious.
Before too long they reach Venom, homeworld of Andross. He taunts them before they reach the surface, where Fox and team battle thousand upon thousand of his warships, and possibly a revived Star Wolf. Fox then enters a maze-like artificial cave and faces Andross alone.
Destroying his false outer face, Fox finds the maniac's true form; a floating brain! "Only I have the brains to rule Lylat!" Andross yells. Unfortunately, he doesn't have the brawn. Fox tears though him, and Andross self destructs in a desperate, vengeful last move. Fox fears he won't make it out in time, until his father James McCloud appears to guide him away from the base. He returns to Corneria to a victory parade, when Pepper offers to place the group in the Cornerian Army. Fox refuses, and the team runs off into the sunset.
This game was called Lylat Wars in Europe, due to copyright reasons. This was also the name of the Nintendo Power comic adapting the game.
Eight years later, we're introduced to Dinosaur Planet, a forgotten world on the edge of the Lylat System. A young vixen named Krystal, who is searching for what caused her homeworld's doom, ends up here after responding to a distess signal. She enters the mysterious Krazoa Palace and finds the remnants of an Earthwalker army inside. The soldiers inform her that they were attacked by General Scales and his Sharpclaw Army, who were attempting to capture Krazoa Spirits for an unknown purpose. She manages to find the first Krazoa Spirit, and places it back to it's resting place. However she is captured inside of a large crystal and becomes helpless. In his process of taking over this world, Scales ends up tearing apart the planet and before too long the matter comes to General Pepper's attention. He informs Team Star Fox (which has only one active member left) of the situation, and they approach Dinosaur Planet. Fox, sole on-duty member flies down to the planet and begins a long adventure to find all of the Krazoa Spirits, vital components of the planet, along with the four Spellstones which hold the planet itself together. He succeeds, and along the way meets Krystal, frees her, and she joins Team Star Fox. At the journey's end, Fox brings all of the Spirits to Krazoa Palace, only to find that Andross has managed to cheat death by infesting the Krazoa God's form with his disembodied spirit. After a long and harrowing space battle in which Falco Lombardi comes to Fox's aid after five years of leaving the team, Andross's spirit and the Krazoa God are both killed, leaving only celebration and peace in their wake.
In Starfox: Assault, it's been one year since Andross was destroyed for the last time. Krystal and Fox are in a pseudo-relationship, and all of the Starfox Team's equipment has been upgraded and repaired. As the Star Fox team is called in to defend Corneria from the Oikonny Rebels, the remnants of the Venomian Army of Imperial Lizards, a disturbing new menace known as the Aparoids invade the Lylat System. Emerging in the heart of the battlefield as Andrew Oikonny, leader of the rebellion, attempts to succeed in killing Fox where his uncle failed, the invaders wipe out much of the fleet. So begins Fox's latest adventure, as he rushes to the Aparoid Homeworld to defeat their Queen.
Star Fox Command
Star Fox Command takes place some time after the events of Star Fox Assault, though it is unclear how much time has specifically passed. It follows members of team Star Fox as they fight the Anglars, a warlike aquatic species that resides in the acidic seas of Venom.
At the beginning of the game, the Star Fox team has broken up, with Fox and ROB being the only remaining members. Throughout the course of the game, Fox will meet up with many familiar characters, including Slippy, Falco, Krystal, Peppy, and even team Star Wolf as they band together to face the forthcoming threat of the Anglar Empire.
The gameplay is very different from other games in the series, as you must control multiple units on a map similar to a strategy game, before engaging in the classic space battles that the series is known for. This also marks the first time in the series where characters other than Fox are controllable during the main game.
Command is also unique in that it has nine different endings that will occur based on choices you make throughout the game. It is for this reason that many fans have speculated that this is the last game chronologically in the series, as it would seem difficult to select a single ending to start the next game from.
Nintendo has stated that this game makes use of certain elements that were originally going to appear in the unreleased Star Fox 2.
Canonically, Star Fox 64 occurs first, with Star Fox Adventures ocurring eight years afterward, and Starfox Assault taking place a year after Adventures. At this point, it seems that Star Fox Command, which has multiple endings, many of which involve the disbanding of the team, is the last game chronologically in the series. It is unclear as of now which ending is the TRUE ending; the only way know for sure is if a new Star Fox game is released explaining how Command ended.
There are also 3 separate comics printed by Nintendo that ran in issues of Nintendo Power that may or may not take place in the series. For the most part, these comics adapt the games, although the third comic tells the story of how Falco left the team. There was also a Japanese manga adapting the third game in the series, Starfox Adventures. It is unknown how canon this comic is as of now.