The first episode has the hero fighting against spider-themed opponents that killed the scientist who rescued him. Just like the first episode of the original Kamen Rider series (though in that case it was only a single spider adversary).
Speaking of the first KR episode ever, Kotaro dwells on his inhumanity by wrenching a water faucet out with his bare hands like Takeshi did.
The SIC figure for Black is actually halfway between his TV appearance and the bulky insectoid proto-form from ep. 1.
Not only is there a spider monster in the first episode (a recurring element in Kamen Rider in general), but all Grongi have their own uniform belt buckles, much like the classic Shocker mooks and monsters do.
Also a bat monster in the second episode, which is also a recurring monster with Kamen Rider in general, though not as much as the Spider.
At one point Yusuke starts wearing a T-shirt with the Kuuga symbol on it, much like Jou Shigeru and his Stronger shirts.
Kuuga's red form being called #4 can be seen as a continuation of the original three riders being #1, #2 and V3.
Sakurako and Jean are based out of Jounan University, the same college where Takeshi Hongo studied; Episode 40 takes it further by having Yusuke, Sakurako, and Enokida mention a "Professor Hongo", who had Big Ol' Eyebrows and a Badass Baritone (Yusuke's impression sounding a lot like Hiroshi Fujioka), implying that they're talking about the original Rider.
The first group of monsters are big cats, and the second are turtles. This homages Kamen Rider V3, where the first monsters of the week were Scissors Jaguar and Turtle Bazooka. Especially fitting because Agito is the second series of the revived franchise, just as V3 was the second series of the original franchise. V3 and Agito also both followseries where the first monsters were a spider and a bat.
Also, the second encounter is often a bat. Guess which Rider Shinji meets first.
Goro sometimes does Rider 1's and Agito's henshin poses as part of his Red Herring routine.
The Double Rider Kick appears a few times: once at the end of the Hyper Battle Video (Ryuki and Agito), and once when Shinji and Ren have to fend off a Mirror Monster unmorphed.
A minor one design wise: Ryuki's eyes, Knight's mouthpiece, and Zolda's antennae all evoke the original Rider.
Though the whole routine isn't the same, Shinji and Ren's henshin poses incorporate those of Rider 1 and Rider 2, respectively.
Ren's first memory on recovering from his Laser-Guided Amnesia (see above) is an image on a woman in a white dress on a beach, just like Shoichi (they were actually Ren's girlfriend and Shoichi's sister respectively).
Shiro Kanzaki went by the name Shiro Takami when he studied overseas. Both names allude to Shiro Kazami, better known as Kamen Rider V3.
The effect of Freeze Vent on CGI monsters like Genocider looked an awful lot like Duke Org Loki's freezing-and-capturing of the Power Animals in Hyakujuu Sentai Gaoranger.
One way to distinguish between the two Alternative Riders is the silver stripes on Alternative Zero, a reference to the primary difference between the first two Kamen Riders (Hayato Ichimonji's suit had the silver stripes).
Shinji and Ren have Rider #1 and Rider #2's poses, respectively.
The Orphnoch King was clearly designed with the Old Gen Kamen Riders in mind, Scarf of Asskicking and all.
The Faiz Edge being a sword with a motorbike handle as a handle evokes Kamen Rider Kuuga; Kuuga's Titan form typically used his bike handlebar to transform into his sword.
There's a lot of old-school KR in this series. The Riotroopers are basically the new Shocker Riders (there are even six of them! Gold armor to go with the Shocker Riders' gold gloves and boots, no less.), and a lot of the technology is classic Rider attacks we willingly suspended disbelief for given a reason to work that way, Batman Begins style. And while it's a bit of a stretch, the Orphnochs are reminiscent of some of the unwillingly-enhanced former human monsters from the old days: All of them were normal people to begin with, a fact the plot gives due attention to, except when it doesn't. Most didn't want the change, and once it happened, some became monsters, some remained themselves and were forced to do things they don't want to by the organization, and a precious few defied the organization and lived to tell. The main Rider is the prime example of the latter. And not everyone survives the conversion process (though Shocker didn't seem to have to kill hundreds to get one monster out of it.)
When Kusaka sees Hanagata again for the first time and demands to know what's going on, he tells him to fight, and keep fighting and winning (and we hear that repeated a few times) and it sounds very much like Shiro Kanzaki. To really hammer it in, when Hanagata steps out in Goat Orphnoch form, we hear the mirror world noise.
Sakuya Tachibana (Kamen Rider Garren) shares his surname with the original Kamen Riders' mentor, Tobei Tachibana, alluding to his role as the most senior Rider in this season.
The red scarf from the Blade Vs Blade video, which nobody but the audience can see.
And Sakuya's former colleague Kiryu had an accident in which one of his arms had to be replaced with a mechanical appendage. Kiryu later retrofits it to release lethal electric currents, thereby referencing both Riderman and Stronger.
Instead of a spider monster in the first episode, we have a spider monster as a recurring villain of sorts, slowly turning Mutsuki evil despite being sealed in card form.
Hajime's Identical Stranger steps into the Cooking Duel with a ridiculous suit of armor, which he calls his Ultimate Form: a term that originated in Kamen Rider Kuuga, referring to the lead Rider of each season's final Super Mode. Not to mention that the armor was mostly black and gold just as Kuuga Ultimate Form was.
Also from Kuuga: the Undeads' belt buckles cracking open upon defeat happened to the Grongi as well (but are a valid plot device this time.)
The story parallels Kamen Rider Ryuki in several ways - ignoring the obvious use of cards, Riders in Ryuki and Undeads in Blade must fight and kill each other until one is left, and the last few episodes see the world swarmed with thousands of bug monsters for related reasons.
One related to it's first Super Hero Time Partner, albeit likely a coincidence - the first episode of this series aired alongside episode 48 of Abaranger, which saw Mikoto Nakadai/Abarekiller die - Kamen Rider Agito was in a similar situation, as it's first episode aired alongside episode 49 of Mirai Sentai Timeranger, when Naoto Takizawa/Timefire dies.
The traditional Rider Kick is no longer the finishing blow of the season, but that doesn't stop our heroes from executing them anyway, from as early as episode 2. Black RX did pretty much the same thing.
Hibiki being utterly crap on a motorcycle (pre-Retool) could fall under this.
And the three primary Oni's special salutes hark back to Godai Yusuke's thumbs-up gesture in Kuuga.
The same thing happened in Kamen Rider Agito, and coincidentally involves another Jerkass meeting another title character for the first time.
The double gold stripes on the Shadow Zectrooper uniforms are a reference to the first Kamen Rider, who was redesigned with double silver stripes towards the end of his series (as opposed to No. 2, who had single silver stripes to differentiate them.) All Zectroopers also carry Arm Cannons reminiscent of Riderman's Cannon Arm, lampshading their status as 'normal' soldiers.
Tendou's Koans always refer to himself as the sun. Kamen Rider BLACK carries the title of 'Black Sun'. And Dark Kabuto's debut is also marked by an actual black sun ie. an eclipse.
In episode 17, Daisuke, accompanying Gon to the women's restroom because she's scared, is caught by a woman, who then opens up her cell phone to call the police. As she dials the numbers, Faiz's phone effects can be heard.
In the documents that are found in Area X, the Masked Rider Project was started on April 3, 1971. This was the air date of the first Kamen Rider.
As pointed out in the design book Imagin: Say Your Wish..., the first few enemy Imagin correspond to Riders from Kamen Rider Ryuki: Bat to Knight, Chameleon to Verde, Crust to Scissors, Crow to Odin, Rhino to Gai. Additionally, as mentioned under Actor Allusion, the Cobra Imagin is designed to resemble Ohja, and is also voiced by the same actor. Sieg also takes after Femme, and got to engage in a Curb-Stomp Battle against Cobra like how Femme killed Ohja.
The Spider Imagin is a double subversion of this - while there was no spider-themed rider in Ryuki,note the only insect-themed rider the show had was the stageshow-exclusive Kamen Rider Papillion, who was butterfly themed it is a reference to the traditional spider-themed kaijin that are present in most series (and was the theme for one of the first monsters fought in the original Kamen Rider).
According to Re:Imagine - Detail of Heroes 03, the villains from Onigashima Battleship are modeled onRiders 1 and 2 (Goludora) and V3 (Shilubara). They also not only draw upon the gold and silver-themed heroes of GARO, but transform the same way.
Kiva Form: Mighty Form (red armored, bare-knuckle all-around fighter)
Garulu Form: Dragon Form (blue armored, speed-based melee form)
Basshaa Form: Pegasus Form (green armored long-range gunner)
Dogga Form: Titan Form (purple armored brute strength form with heavy weapon)
Emperor Form: Ultimate Form (gold armored Super Mode with the power to use all past forms' weapons (for Kuuga it's All There in the Manual) and a dark counterpart (Dark Kiva and N-Daguba-Zeba respectively).)
Lampshaded in Decade when Tsukasa gets into a fight with an Alternate Universe Wataru, using each of Kuuga's forms to match up with their respective Kiva forms.
Kiva also contains some nods to Kamen Rider Agito - Garulu and Basshaa Form are asymmetrical, just like Agito's Flame and Storm Forms, Garulu and Storm have their own set of similarities (blue, left-handed melee fighter), and of course DoGaBaKi Form corresponds to Trinity Form, both being mish-mashes of their respective Riders' alternate forms and using All Your Powers Combined-empowered Rider Kicks as their finishers. Additionally, in the early parts of the series Wataru tends not to talk when he's in the Kiva suit; Shoichi was much the same in Agito.
The origins of the four Riders in Kiva also mirrors that of the four Riders in Agito - Magic Based Primary Rider, Technology Based Second Rider, Incomplete version of the Primary Rider, Alternate Version of the Primary Rider.
Also, the spider-monster in the first episode, who's an Ascended Extra of sorts this season.
IXA's weapon works just like Kaixa's (a plus shaped weapon that changes from a gun to a sword), they both have a phone Transformation Trinket (although to be fair, IXA's phone is for his most powerful form), and just look at their names! Not to mention that the one who uses it the longest is... not allthere.
Even better, Saga's belt copies the spinning hub and rod in the side from X's belt.
At the end of The Movie, there is a shot of a bunch of mascot costumes goofing around, four of which were the same ones the Taros wear in one of Den-O's own movies, Final Countdown. The one wearing Momotaros's dog costume was even holding a sign that reads "Yakisoba Sanjou!".
Taiga's costume of a white jacket and a black glove on one hand resembles what Minami Kotaro wears in Kamen Rider BLACK RX: a white jacket and a white glove on one hand.
Kamen Rider G: The short version is "everything" (even the recycled music is used under the same circumstances as in the original series) but they went the extra mile with the transformation, which is basically a Continuity Cavalcade in a Transformation Sequence. First, he lands, imprinting his symbol into the ground a la Kiva. Then, he does Kamen Rider 1's arm-fling, then rotates it with his arm leaving behind an afterimage just like Skyrider. He inserts the wine bottle from the side just like Ryuki's Advent Deck insert, and pulls the corkscrew lever back much like Gatack's Cast Off. The suit's red lines appear first and trace around him exactly like Faiz, and then there's a sort of liquid explosion effect just like Chalice. The helmet is last to appear (X-Rider homage, or is that a stretch?) after which the eyepieces light up and there's a ripple of heatwaves, similar to Ixa when his mask opens.
There is one very subtle reference: The physical transformation ends with the costume in a darker burgundy purple scheme, which bursts into a brighter crimson red when his eyes light up. It's similar to how Kamen Rider 1 and Skyrider started their shows with darker costumes before getting a lighter one, as well as Black and his 'grasshopper monster' intermediary form. (Unsaid in the episode itself is if the burgundy version is his 'evil' form from when he was still with Shade.)
Three of the miscellaneous books seen in Chapter 7, used to unlock Avalon, have similar titles and covers; are based on Momotarō, Urashima Tarō, and Kintarō; and are colored red, blue, and yellow respectively. Putting those three tales in a set with those colors makes a clear reference to Kamen Rider Den-O, with some of that series main Imagin based on the same tales and colored the same way.
Another one of the books used in the ritual is Osha Jizou San, based on the story of Kasa Jizō. On its cover, the frontmost Jizō statue is wearing the Ore Parka Ghost.
The Yeti Megid is the first Monster of the Week of 2021, evoking the original series' appearance of Shocker's yeti-themed monster, named Snowman, in the very first New Year episode back in 1972.