F-Zero/WMG

Most of the races take place on Earth
If Mute City in F-Zero is New York as we know it now, that means that at least some of the races take place here on our home planet. But in F-Zero GX's story mode, we're never given any indication that Falcon ever leaves the surface of one planet, meaning that it all took place on one world. Here are where some of the courses are: Red Canyon is likely the Grand Canyon, as there is a river running through it. You can see the river in the Red Canyon story mode course, in Chapter Two. Big Blue was once a city attached to a continent, likely the American West Coast. It was likely Paradise City from Burnout Paradise, which became Pacific City, from Crackdown, which became Oceania, from Extreme-G 3. Port Town may be San Francisco, or any number of other West Coast cities, making Captain Falcon an American. This means that in F-Zero, Earth Is the Center of the Universe.
 * This may be partially true; Silence, at least, is a different planet (It's stated in GP Legend that Silence has no inhabitants, hence the name) Phantom Road is likely some random area in space, Outer Space probably is too. The other areas are all on the same planet, most likely. Unless you seriously believe GP Legend and think that Mute City covers the entire old earth like the map screen in story mode suggests.
 * The GP legend games and anime take place in a separate continuity from the main games. I mentioned F-Zero GX, which is a main game. I don't believe that Mute City could cover the entire planet. However, we never have received any indications against Earth being the location of multiple racecourses.
 * Except that it's All There in the Manual that this isn't true. It's all on different planets.

James McCloud is actually from the Lylat System
Think about these two facts:
 * They share a technology known as the "G-Diffuser" system. In F-Zero, it's used to keep the race crafts off the ground(If only just); in Star Fox, it's used to keep flight craft aloft.
 * One character from each series is named "James McCloud". He suffers a Death by Origin Story in Star Fox, but he's still there in F-Zero. Maybe the two are related?

Andross may have thought that turning him into a full-fledged human would be A Fate Worse Than Death. Sending him off to Earth, an unfamiliar place, would have been the icing on the cake. James also had his memory erased, and he only remembers his name. The squadron "Galaxy Dog" was just a cover story, implanted in his mind just to give him a reason to own the ship he was given. However, knowledge of the G-Diffuser technology has awakened some old memories, and James is now thinking to what his life was in Lylat. He will eventually uncover the truth...

The game takes place in the Mega Man universe
Mute City could totally be the city where Mega Man and co. lives, or the first level of Mega Man X (or, well, any city of the series). This is also why you can die so easily : either you are falling in a Bottomless Pits or on Spikes of Doom.

Mute City, Port Town, and Red Canyon are all futuristic versions of notable places in the United States.
This is going off of the anime, which states that Mute City is New York City... in the future. In the Story Mode of GX, Captain Falcon starts off by training in Port Town. The next day (Chapter 2), he bumps into Samurai Goroh while riding through Red Canyon. After winning, Falcon speeds off to Mute City and arrives there by sunset.

Now, this is just conjecture on my part, but if Mute City is indeed The Big Apple, then my guess is that Red Canyon is the Grand Canyon and Port Town Town is somewhere on the West Coast, presumably California. Think about it. NYC is indeed a very important trade center for America, in the same way that Mute City is the center of trade and commerce in the galaxy. I'll let you do the math with the Grand Canyon.

As for Port Town being on the other side of the U.S., the F-Zero machines (as of GX) cruise around at a default average of 1000km/h. That's pretty darn fast. If Falcon left Port Town in the morning at those kinds of speeds, he probably could make it to the East Coast by sunset. And yes, that is factoring in the short "race" he had with Goroh.

However, I have no clue where that places Lightning and Aeropolis (the former being a short distance outside of Mute City according to Story Mode; the latter is presumably also on Earth).

The game takes place in the Lylat System in an Alternate Universe.

 * Both have a James McCloud, but one is a human and the other is an anthro fox. Two of the prominent racers in F-Zero drive machines called Golden Fox and Blue Falcon; The Hero and The Lancer of Star Fox are a golden fox and a blue falcon. Also, one of the endings of Star Fox Command has said hero and lancer quit their mercenary work and go to race in the Lylat GP...also known as the G-Zero GP. The similarities are staggering.
 * Not to mention that both series power crafts using the "G-Diffuser" propulsion system. And both take place in a universe where fantastic technology, interstellar society, and hidden magic forces all exist simultaneously. Also, Captain Falcon has an evil twin/rival, much like a certain furry pilot. And both series have their share of mercs, bounty hunters, and space bandits. And hey, while we're at it, Great Fox, Falcon Flyer? If it's not an alternate universe, then it's either one of the biggest collections of inter-series references Nintendo's ever amassed, or a hell of a coincidence. On the other hand, maybe Nintendo just really likes using this stuff.

Captain Falcon has a counterpart in an alternate universe
Who drives a bike rather than a car, never removes his helmet with incorporated Cool Shades, whose blue uniform with eagle motifs is instantly recognizable, who has a gun and uses it, whose punches are legendary, whose mighty chin is the most you see of his face, who chases criminals for a living...

F-Zero is the Professional Wrestling of the future
Given the Lucha Libre inspirations of some of the characters, the outlandish backstories and rivalries, the fact that racers can be "retired" in fiery explosions but still show up fine for the next race, and F-Zero GX's TV Interviews (with characters that would probably not be willing to conduct such a thing), it's not too far to assume it's choreographed.
 * Additionally, Black Shadow's Master Class video in GX (more or less a blooper reel, complete with Deathborn apologizing to an injured Black Shadow after throwing him into the camera) would suggest that the characters are Animated Actors.
 * And Zoda blatantly admits to cheating, and Blood Falcon casually talks about either killing or murdering certain people, and talks about avoiding his arrest.
 * That would also explain why Blood has a different voice from Falcon despite allegedly being his exact genetic duplicate. For all we know, the backstories and rivalries are just fabrications to make the characters interesting (for example, the Arrows could be a Kayfabe couple instead of real life spouses); the Truce Zone seen in Chapter 3 of GX's story mode (where everyone is seen drinking and chatting at the Bet Race diner) perhaps verifies this.

The series will see a revival on the Wii U.
Explained here.

The next game will use the Hedgehog Engine
It's most likely that the Wii U will be the next destination for the new F-Zero, and the Wii U should be powerful enough to handle the engine. Also, F-Zero is the only other series besides recent Sonic games that have fast enough movement to take advantage of the engine, and Sega had a hand in GX.