Broken Base - The issue of whether the later series are as good as the older series, for starters.
Wizard and Gaim are both massive divisive seasons, though for separate reasons- Wizard is derided by some as playing it safe with the franchise and having a bland protagonist, but is lauded for the great effects in the fights and likable side-characters. Gaim, on the other hand, is derided for being too dark, having too many characters to keep track of, and having one of the bleakest stories in all of Tokusatu, which had some calling Darkness-Induced Audience Apathy. Alternatively, some love the Darker and Edgier approach and say it's given Kamen Rider its best characters ever.
Whether or not the series should get a Power Rangers-esque adaptation - proponents will point towards Kamen Rider Dragon Knight as an example of how to adapt the series properly, as well as point out that if there was an American KR franchise, merchandise would be released over here, and the source material would likely be released similar to how Shout Factory is releasing the Sentai series; opponents, on the other hand, will point towards Saban making the show more appropriate for kids, and also point towards the OTHER American Adaptation as a counter-argument. Still others would prefer a subbed version release on an anime streaming website like Crunchyroll. Others still would prefer a Hong Kong Dub over just subtitles.
One of the longer-running ones is the Neo-Heisei number theory. The first few such series (Decade to Fourze) had very clear numerical themes, with the number incremented by one every year (Decade's number was 10, but easily serves as 1 in the pattern; Double was "two Riders in one" and used two Memories at once, OOO's Medals came in threes, and Fourze was named for 40 Switches ("Four-zero") and used four at a time). A number of fans believe the theory that Toei kept on incorporating the theme even when the Rider's name and number of trinkets didn't reflect it, though just as many think that said believers are only seeing the theme numbers because they want to find the theme numbers, not because said numbers are there on purpose. Thankfully, the theory died down over time, as there was little discussion over any presence of tens in Build.
To a lesser extent, there's "Power Rider", a trademark Saban filed...but never did anything with. Was Saban intending to adapt Kamen Rider a second time? Was it just a trademark they filed so it couldn't be used? Or was it something else entirely?
Fridge Brilliance: Since Skull was chronologically the first Rider to appear in the Double-verse, it could be argued that the Spider and Bat Dopants actually were the first MotWs in Double. And since chronologically, Skull was active before all Heisei ridersnote Skull was shown to first be active in November 1999, 2 months before Kuuga began, that would make the Spider and Bat Dopants the first MotWs for the entire Heisei (and Neo-Heisei, if you believe there's a dividing point) era.
Friendly Fandoms: With both the Super Sentai and Power Rangers fanbase. The former for being sister series and having different yet equally valid interpretation of their genres and the latter for helping them being introduced to the greater toku genre and their shared hatred of Sabans Masked Rider.
Which is weird, because the backstory of that show happened in canon; the Rangers were even on Edenoi with Dex.
Although the Retcon does erase the series out of canon, it does not do the same for the pilot, since A Friend in Need happened in Mighty Morphin, and the part would later be referenced in Alien Rangers of Aquitar. In-Universe, it's entirely possible that the show seen in Time Force was created based on Dex's adventures (i.e., he wrote about them in a book, or the show was made as a biography with him playing himself).
Narm Charm: The series BREATHES this trope. When you can take a bunch of dudes doing Wire Fu in ridiculous jumpsuits against rubber monsters seriously, THAT is an achievement. Taken Up to Eleven in Kamen Rider Gaim, where the plot is about Riders in dance teams using powers themed on fruits, yet it STILL manages to be awesome. And serious. And very dark. Of course, the fact that Gen Urobuchi wrote it probably had something to do with it.
Paranoia Fuel - Ryuki. Just think about it. Every mirror - hell - every single reflective body you walk past could be a portal from which a monster whose only desire is to eat you could emerge from. And don't think it's just that odd piece of glass in the streets, or that puddle of water you need to worry about either. Every mirror is fair game, even the ones in your home. Really, the only guarantee of survival in the Ryuki world possible if you were just a 'normal' is to lock yourself in at home and cover up every piece of glass.
...Or if you somehow found a discarded deck like Shinji did.
The monsters are essentially relentless, and will never stop hunting you once you are chosen as a target. Lousy luck if you're in the dark about, but if you are aware of their existence..... This applies to Dragon Knight as well, with the trade off of mindless monsters that will eat you at the first opportunity for an organized force that is just waiting for it's shot at conquering the whole damn world, and if not for the Riders, would have succeeded.
We should also count the series where the monsters can take human form. like the worms of Kamen Rider Kabuto. They kill the original, and take that person's place. An impersonation so good, that they can fool anyone, including THEMSELVES! This means that anyone you know, Father, Mother, Best friend, ANYONE could be a worm in disguise. Lovely thought.
Shocker is everywhere. If you are in their sights, whether it be a random target or worse, if you're a witness, they will find you. Your home is no longer safe, your friends might be monsters in disguise or already dead, your drinks might even be poisoned—No matter what you do, they will always be five steps ahead. Sure, Kamen Rider 1 or 2 can save the day, but lord forbid you're the first victim of the episode. You know, the one nobody ever saves...
The Imagin from Kamen Rider Den-O - you think that the worms are bad? At least the worms are restricted to what time they show up; the Imagin could've potentially gone back to when any previous rider series took place and wrecked havok. Unless you happen to be a singularity point (something which seems to be very rare), if one forms a contract with you, you'd better hope it's a benevolent one, otherwise they'll go back in time and pretty much rewrite the present as you know it.
They Wasted a Perfectly Good Character: Or rather, an organization - Foundation X could've easily filled the role of villainous organization that Shocker has filled in almost all the post-Double works involving Shockernote the only real exception would've been Kamen Rider 1, since that was heavily focused around Ichigo...yet after Movie War Megamax, they've pretty much been Demoted to Extra, with the only thing they played a direct part being the "Beast Rider Squad" special of Kamen Rider Ex-Aid. Their absence is especially jarring in Movie War Core, considering that they were also shown to be interested in the medals that Kamen Rider OOO uses.
Former Nazi, Colonel Bakarashin Iinodevitch Zol, joined Shocker and quickly gets a reputation for brutality. Transferred to Japan to deal with Kamen Rider 2, Zol brainwashes children into become Shocker troops and gases an entire town. Apathetic to the fates of his own soldiers, Zol dismisses their deaths and even tests the powers of a resurrected mummy-like kaijin by letting him murder one of his mooks. Using another infectious kaijin, Zol has him kill a group of innocents, forcibly converting the survivor into a disease-carrier to spread more suffering. In the sequel series, Zol works with Doctor G to unleash toxic gas in Hokkaido and killing the innocent civilians.
Fridge Brilliance: Shocker is established to have ties to the Nazis, with several of it's key members having been Nazi officers. The Great Leader of Shocker is implied in later series to be an evil spirit powered by and sustained by human evil. Is it any wonder the guy first surfaced, that we know of, after the atrocities of WWII and brought many Nazi officers along with him?
"Seinfeld" Is Unfunny: Although not to the same extent as Goranger, it's a bit jarring to watch this series if one was introduced to Kamen Rider through one of the Heisei-era shows - while it does have a secondary rider, initially the secondary rider acts more as a replacement as opposed to a supporting character, the lack of Swiss Army Heronote although this is less prevalent if one was introduced to the franchise with a Heisei series that aired in-between Agito and Den-O, the main character having a permanent upgrade to gain more powers as opposed to a Super Mode they can transform in and out of, and the fact that the main character's powers come from him being a cyborg as opposed to getting his powers from other sources.
Special Effects Failure: Granted, it's an old series, but there are a lot of moments where it really tends to show its age.
This was partially justified by the fact that the show had a very low budget even for it's time.