The first Red Faction game takes place on Mars, where a group of miners rebel against Ultor because of the horrible living conditions they have to face while on Mars. By the third game, Ultor is long gone and all that is left of it are a few ruins of Ultor buildings.
The Saints Row series features many references to Red Faction, but Volition have confirmed that the Saints Row and Red Faction universes are not linked, and that the Ultor references were only intended as Easter Eggs.
The Ultor corporation in Saints Row was a peripheral company who sponsored the Ultor Dome and had some Clothing items. In Saints Row 2, Ultor is a main antagonist. Ultor continues making appearances throughout the series.
Parker is the name of the main character from Red Faction.
In Saints Row 2, there's a radio advertisement for a TV show called Red Planet, Red Passion, a drama series about miners on Mars. It mentions a character named Parker, and a character named Eos, another character from Red Faction.
In Saints Row 2, while inside the pyramid facility there is a PA announcement that says "Parker please report to the mining facility." Red Faction takes place in a mine on Mars
In Saints Row 2: Ultor Exposed, there is a vehicle named the EDF Scout, which are used to scout out hazardous mining areas. When The Protagonist asks where such equipment would be needed, Tera says that he wouldn't believe it if she told him. The EDF are the antagonists of the then recent Red Faction Guerilla. The vehicle is almost identical to the vehicle in that game, except for a different turret.
on the very top floor the Stilwater Science Center, there is a model of an EDF Flyer from Red Faction Guerrilla. These also appear in the mission "Gangstas in Space", the Tails of the Flyers have EDF markings.
The symbol of Red Faction: Guerrilla and Red Faction appear as logos that can be applied to clothing.
Read Fiction Used Books - a store in Sommerset whose sign is similar to the Red Faction title and logo.
RFS - Radio Free Stilwater, an unused Radio Station whose logo is similar to Red Faction's logo.
In "The Fight Before Christmas" the Elf Resistance has painted a symbol similar to the Red Faction logo on several buildings, consisting of a green fist clenched over a candy cane in the style seen in Red Faction: Guerilla.
Gangstas in Space Speech
In the final cutscene of the mission "Gangstas in Space", The Protagonist gives a speech the same as the speech given by Alec Mason, the protagonist of Red Faction: Guerrilla, in the final cutscene of that game. Reinforced by how Male 1's voice actor is Troy Baker, the same person who voices Alec Mason in Red Faction: Guerrilla.
The Unicorn who can fire destructive rainbows from it's rear (who is utilized as a weapon in Red Faction: Armageddon) is featured on a green logo on the ground in one of the STAG bases.
During the mission "De Plane Boss" a mock introduction to a film titled The Inevitable Rise and Fall of Johnny Gat is said to be a Mason Brothers Production. In Red Faction: Guerrilla there is a playable character named Alec Mason (who is voiced by Troy Baker who does the default Protagonist in Saints Row: The Third and Saints Row IV) and has a brother called Daniel Mason.