The rooftop trainings are based heavily on the scene where Morpheus trained Neo in the art of the super jump.
Super Ben King is Morpheus.
In the real world, humans are being kept in red pods, totally naked, immersed in goo.
Also in the real world, the main weapons of the resistance are Mini-Mecha.
There is a traitor who gets the heroes ambushed in the virtual world and nearly killed in the real world.
Not only is it a parody but it actually goes through the history of the Matrix. The first sim you are stuck into is an idealistic paradise similar to that described in the films. It's excessive perfection - a "sunshine and rainbows" 1950s-era sitcom, in the Boss' case - immediately makes the boss suspicious as they try to fight their way free of its restrictions, such as being unable to exceed the speed limit or drive dangerously.
A scene of the Boss leaping across a gap with Keith David catching and pulling him up in the "War for Humanity" trailer is a nod to the Suicide Mission of Mass Effect 2 (Keith David having voiced Captain Anderson in said series just reinforces the Shout-Out).
Also, every homie has loyalty missions and romances. Although the romances are hilariously parodied. The suits in the real world look a bit like Shepard-Commander's gear too. And the intro mission where the Zin Empire abducts everyone has a lot in common with the mission where Joker has to get to safety from the Collectors.
In the text adventure you could investigate a planet then launch a probe for resources. How did you progress through the game again?
The moral choices while walking through the White Crib are a big parody of Paragon & Renegade action prompts. Include one for punching someone (although in this case both choices punch the victim, just in different places).
The bill to cure world hunger, which Keith is holding up, reads "Let them eat cake" in reference to a quote famously attributed to Marie Antoinette.
Though these are also possible references to Fable III which more or less has the player character a King/Queen make similar decisions.
The game tells you that you have to have done all the loyalty missions of your homies to get the best ending. Also in the final mission, you have to pick a different pair of homies for three different sections, and your choice has some effect on the results.
The game provides a Lampshade Hanging with the line, "It's not every day that you get to kill aliens with Keith David."
The opening cutscene in "The White Crib" before the alien invasion is very reminiscent of the "Walk and Talk" shooting style The West Wing became famous for. Considering the mission is called "The Saints Wing"...
The first mission is a slightly different take to traditional Saints gameplay... Call of Doody perhaps? Modern Whorefare? Rather than the Affectionate Parody of other games Purple Ops/Zero Saints Thirty is a rather serious (and awesome) take that closely mirrors the games. All the way down to to the breaching scene. You can even go commando aka the multiplayer perk as the melee is a One-Hit Kill knife.
The nuke-climbing section near the start, the flying-a-spaceship-through-another-spaceship section, as well as Zinyak's appearance and tendency to telepathically hold the protagonist, are somewhat reminiscent of Halo 4.
The nuke-climbing and -disarming sequence, with Aerosmith's I Don't Want To Miss A Thing playing, is an obvious Shout-Out to Armageddon, involving a similar sacrifice to manually detonate a nuke, instead of disarming one.
Flying through the ship is very shout-out-y to The Matrix. Especially the Animatrix episode title Final Flight of the Osiris. It's also almost identical to the last mission of Enter the Matrix, first from Niobe's perspective (flying the ship right after breaking out of the simulation) and then Ghost's (the turret section after Matt's rescue).
The mission in the "paradise" version of the simulation world starts with Leave It To The Saints popping up on the screen as you slide down a banister to a jaunty sitcom tune and even follows up with "Brought to you by..." ad.
Also, being placed in a virtual reality of sunny, quaint American town from the fifties bears uncanny resemblance to the 'Tranquility Lane' simulation from Fallout 3.
The clock tower in the 50s simulation is stuck at 10:04 and has a cable running from it to a nearby pole.
It is later used in How The Saints Saved Christmas as a conductor, making the reference more obvious.
Taunts and compliments contain several examples, including:
Don't forget that there is a hairstyle that is obviously referenced to Dragon Ball, that (painted gold or black) and the karate outfit with the appropriate colors, you can make yourself look a bit like Goku!
And then there's a reference to a certain red baseball cap worn by the villain fromParanoia Agent. Strange reference considering it's so obscure in comparison to others, and doesn't have the little buttons.
Many of the weapons [skins] are shout outs to movies, tv shows, and other games such as:
EM Railgun◊ - Reference to Eraser. Too bad you can't dual wield them like Arnold did.
Impulse Rifle◊ - Reference to the primary weapon of choice for the Colonial Marines from Aliens.
El Fugitivo◊ - Reference to Desperado and its related trilogy. Though this one fires "backwards" from the one in the film.
Tiny Pistol/Loud Locust◊ - Reference to Men In Black. You can find it in the basement of Let's Pretend. Like its MIB counterpart just firing it knocks you down but it pretty much destroys everything in front of you in the process.
Going even further the mission has you up against your evil twin. Like a certain main character and his evil "twin" in his own game.
The evil twin has an evil goatee (even if you are playing a female character) because everyone knows evil twins◊ have goatees◊!
Really, the entirety of Asha's recruitment mission is an Affectionate Parody of Metal Gear, riffing everything from patrolling guards, to air ducts, death codecs, alert signals, evil clones with eyepatches, and the morality of killing lightswitchs (he had a family dammit!).
Also, the fact that Asha pictures The Boss is the main villain of that mission makes a lot more sense when you look at their name.
"Look, I was told to walk in a certain pattern, over and over, until something interesting happens! WELL I DON'T SEE YOU GETTING A JOB!"
One of the Ultor guards during this section even says "Baby, my snake is 100% solid!"
When the Boss first gets to play with the power armor, they question why Kinzie couldn't get the guns working in time for them to raid the Zin mothership. In response, Kinzie argues that what she does in the simulation, she can't do in the real world. "I can't just wave my fingers, and 'oooh, look Kinzie, you weave worlds like a goddess with a brush!'"
There are several Ghostbusters refs in Pierce's rescue mission.
Paul was essentially a Saints Flow version of the Stay Puft Marshmallow Man from the first film.
Taking control of a national monument to fight the evil spirit mirrors the climax of the sequel, replacing the Statue of Liberty with the Steelport statue of Joe Magarac.
One of The Boss' lines during this segment is "What did you do, Pierce?", mirroring Peter Venkman's line from Ghostbusters, asking Ray what he was thinking about before the Marshmallow Man came onto the scene.
If you call Ben King and C.I.D. as homies, Ben will question C.I.D. about his name. The AI explains that many great quests involve a person named Cid, "like the last fantasy game I played."
The obligatory Buffy the Vampire Slayer reference crops up, of all the places it might, in the Saints of Rage riff. The anti-drug message is from Josh Birk, who plays Nyteblayde, or rather Angel and his occupation is listed as vampire slayer.
The name of the power armor you unlock at the end? Iron Saint!
The sprint and jump effects and animations are very similar to those used in Crackdown.. Collecting the data clusters is also similar to collecting the Agility and Hidden Orbs.
Also the glide mechanics and some of the superpowers are rather similar to Prototype.
The sound effects to powering up your jump and the sounds as you super sprint are very similar to those used in The Matrix sequels as Neo jumps into his super flight and flies at super speeds (similarly having cars and other debre caught in his wake).
One takedown kill involves a very Albert Wesker-ish move where The Boss impales an enemy's torso with their bare hand and then lifts up the corpse with a smirk.
The idea of a US president in a mecha and kicking butt is itself a reference to a previous game.
There is a reference to the Man with No Name from the Dollars Trilogy. His clothing appears in stores, named "The Hat With No Name" and "The Suit With no Name".
In "The Saints Wing," the Boss accesses the hidden gun cabinets in the Oval Office by flipping open a bust of Johnny Gat and pressing a button in the neck. This is the same way Bruce Wayne accesses the Batpole in Batman, except there the bust is of William Shakespeare.
In "Psychosomatic," the Boss and the Shaundis face a horde of duplicate Veteran Childs with superpowers, each of whom grow stronger when one of their number is killed. Minus an Alternate Dimension angle, that's the premise of The One.