There's a stigma around time-travel stories. For good reason, right? There's a lot of shows that go fast and loose with time travel - and in the process, create problems that they're unwilling to rectify. Weaker episodes of famous time travel stories such as Doctor Who get caught up in these logical hoops, caught between the necessity of a logical plot, and the importance of emotional storytelling. An effective time travel show, therefore, has to decide on rules about its premise that work with the emotional heart of the story, not against it. Does time travel affect the present, and the future? Can anyone time travel to any time? What happens if you meet yourself?
I think the way that Den-O deals with this problem is both elegant and thematically poignant. In the world of Den-O, memories themselves are what create the past. The past can't be changed if there's someone left who remembers how things are supposed to be. These people who can remember changes to the past are called singularity points; meddling in time cannot affect them. So, the only way to change the past (and therefore the future) is to eradicate any problematic singularity points first. This is the crux of Den-O's plot, and I think it's a beautiful concept.
As a singularity point, Ryotaro is able to become Kamen Rider Den-O, the protector of time. His enemies, the Imagin, come from a destroyed future, and seek to change the past in order to destroy and reclaim the future of Ryotaro's timeline. The heart and soul of Den-O is the pain of being a singularity point. If somebody is completely forgotten in the present, they won't come back even if the flow of time is restored. And should this happen, Ryotaro and the show's other singularity point, Hana, are alone in remembering the 'true' state of things. It's a jumping point for striking questions. Would you rather know someone you love is gone, or never know they existed? This point is reinforced with Kamen RIder Zeronos, Sakurai Yuuto. His power as Zeronos literally comes from erasing people's memories of him. One story arc focuses on Deneb trying to create new memories for Sakurai. In doing so he makes a girl forget about the good times she had with Sakurai. Only when he realises the pain he caused her does Deneb realise why Sakurai doesn't let himself become friends with people. She may not know what the lost... but she still lost it.
Before Den-O, i'd never seen a show that so eloquently and heartrendingly uses time travel as a tragic curse. For that alone, it's easily one of my favourite Kamen Rider shows, if not one of my favourite shows ever.
I'm not alone in loving Den-O. It was a hit in Japan on release, and has EIGHT movies. An average season of Kamen Rider gets maybe two, if it's popular. Eight is ridiculously unprecedented. And that number doesn't even take into account other riders' crossover movies where Den-O plays a main part, like Heisei Generations Final. The main reason for this ongoing popularity is its incredible cast of imagins. The four main cast of Momotaros, Urataros, Ryutaros and Kintaros steal the show whenever they're on screen, which is often. Momotaros especially was an ensemble dark horse and often appears in crossovers without Ryotaro at all. Their careful balance of comedy and familial bonding is a joy to watch, which has kept Den-O ridiculously popular in fanpolls up to the present day. Some people say that it's only popular because of the characters, and that the plot is weak. I strongly disagree. Den-O's plot is the reason why the characters are so beloved; the difficulties they face, and the troubles they overcome together are what makes them so wonderful. Deneb is a personal favourite of mine. He's Yuuto's surrogate mother in a sense, fussing over him and protecting him as best he can. He matures alongside Yuuto, accepting what he cannot change and fiercely protecting those he loves. Seriously, there are no bad characters in Den-O. Not a one. (Okay, Kai is kind of weak as a villain, but the absolute catharsis of his defeat makes up for it).
It would be remiss of me not to mention the flaws of Kamen Rider Den-O. Every Kamen Rider show tends to fall into the same outdated portrayals of women, of which Den-O is no exception. There are no female Kamen Riders in the show, and only three women in the large main cast - Hana, Naomi and Airi. Of over 40 Imagins, around three are female - and none of those are good Imagins that get ongoing screen time. Instead, it's a man's show, with Hana and Airi as supporting cast, and Naomi occasionally presented as eye candy due to her actresses' beauty and popularity. This is not a problem unique to Den-O, and is generally a constant in Kamen Rider shows. There is one example of Den-O moving the franchise forward, however: The special movie 'Pretty Den-O' is the first Kamen Rider movie to star a female protagonist, who is a Kamen Rider to boot!
I'm always extremely ready to recommend Den-O as a first rider show for beginners. It's a perfect balance of early heisei's melodrama and neo-heisei's lighthearted action. I would especially recommend it to fans of Shonen anime, as it leans into the monster of the week style.