Yu-Gi-Oh!, on TV Tokyo
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Caution: Spoilers
Season 1
The show started out kind of meh... it's just a card game. Early on I didn't have high hopes for it, but it got better later on. Of course, one thing never changes: all the duelists talk way too much; it seems like at least 75% of any duel is comprised of trash talking and/or moralizing. But anyway, the show's potential lies in the fact that the card game is actually based on some ancient Egyptian magic and stuff. And there are these seven magical "Millennium Items," which can give their bearers great power.
The main character is like this teenaged kid named Yugi Mutou, who plays a card game called Duel Monsters, which his grandpa Solomon has taught him. One day, Yugi put together an item called the Millennium Puzzle, trapped within which was the spirit of an Egyptian pharaoh from 5000 years ago, who has lost his memories. Now the Pharaoh's spirit will share Yugi's mind and body, though when the Pharaoh is dominant (as Yami Yugi, see paragraph 5 for info), Yugi looks like the Pharaoh. It's hard to tell the difference, though, because he looks just like Yugi, except a bit older. They're both fairly short, though, so he doesn't get much taller when he transforms.
Anyway, there's this guy named Maximillian Pegasus, who created Duel Monsters, and he's having this big tournament for the best duelists in the world, on his secluded island, Duelist Kingdom. And to ensure Yugi's participation, he has used the magic of his Millennium Eye to trap Solomon Mutou's soul in the Shadow Realm. And so Yugi goes to the island, along with his best friends. The only other real duelist amont them is Joey Wheeler, who wants to win the prize money to pay for an eye operation for his sister Serenity. Their other two friends, Téa Gardner, and Tristan Taylor, are mostly just along for moral support. Another duelist we see a fair amount of in the series is Mai Valentine, who becomes a friend to the group, but still a rival, and fairly independent. I suppose I'd be remiss if I didn't also mention Weevil Underwood and Rex Raptor, a couple of duelists who will occasionally make trouble for Yugi and the gang throughout the series. And then there's Seto Kaiba, who owns KaibaCorp, which creates all kinds of technology, most of it for new ways of playing Duel Monsters. And he's like the best duelist in the world. And Pegasus traps his little brother Mokuba's soul in the Shadow Realm, too. (Mokuba will become a friend of the gang, but his brother Seto never really does.) Pegasus wants to take over KaibaCorp. And then there's this boy named Bakura, who goes to the same high school as Yugi and his friends, and is on the island as a duelist, himself. And he turns out to have a Millennium item, too, the Millennium Ring. Which contains the spirit of some evil guy from 5000 years ago, who possesses Bakura (Yami Bakura). Eventually Yugi wins the tournament, and the title "King of Games" (which is what "Yu-Gi-Oh" means, I guess.) For the rest of the series, Kaiba will be obsessed with winning that title back from Yugi.
So anyway, it's all kinda complicated and as I say has potential for deep drama and stuff, but aside from the Millennium Items and all the Shadow Realm stuff, it's still mostly just about a card game (and an attempted corporate takeover). Although there's some other stuff after Duelist Kingdom, like meeting a little girl named Rebecca Hawkins who is also a Duelist and will later become a friend of the main characters; and she's the granddaughter of Professor Arthur Hawkins, who is an archaeologist and an old friend of Solomon's. We'll see more of them in future seasons. And then there's a brief arc where our heroes get trapped in a virtual reality world while five members of KaibaCorp's board try to take over the company. And an arc where we meet Duke Devlin, who is plays both Duel Monsters and Dungeon Dice Monsters. He'll become another friend of the gang, who we'll see on occasion. Anyway, that's the first season.
Season 2
The second season deals more with the ancient Egyptian connection to Duel Monsters. Kaiba sets up a tournament of his own called Battle City, after being told by this woman named Ishizu Ishtar that he was the reincarnation of this guy who fought the Pharaoh thousands of years ago. At least, I think that's what she said, but after seeing the final season that doesn't make much sense. (Ishizu, by the way, has an item, the Millennium Necklace, that lets her see the future.) She also tells Yugi that he is the reincarnation of the Pharaoh. Or maybe she just said that the spirit that lives in his Millennium Puzzle is the Pharaoh, I dunno. It's hard for me to remember a lot of these things that happened so far back now, but I think maybe in the first season they didn't even know that much about him. I also thought she called him "Yami," but that's not his name (though I thought for quite some time that it was). "Yami Yugi" just means "Dark Yugi," and it's used to differentiate regular Yugi from Yugi when the Pharaoh is dominant. There are other characters in the series who sometimes have "Yami" appended to their names, if they're possessed (unlike Yugi, who merely shares his mind, willingly).
Anyway, Ishizu's family has been guarding the Pharaoh's tomb for thousands of years, but now her brother Marik (who has the Millennium Rod) wants to steal the power of the Pharaoh (along with all seven Millennium Items) for himself, and controls a group of Rare Hunters who seek out the rarest Duel Monsters cards to increase their power. And Bakura's still out there possessed by some ancient spirit in his Millennium Ring, I guess. Also there are 3 Egyptian God cards, and Kaiba has obtained one but wants to use his tournament to obtain the other two, because these are like the 3 most powerful cards in the entire game. That's really all he cares about, because he doesn't believe in magic or reincarnation or destiny or any of that. And he thinks Yugi and his friends are fools for believing in it, and he also doesn't believe there's some ancient Pharaoh sharing Yugi's mind. Meanwhile, Marik also wants to get his hands on the God cards. But Marik is possessed by... an evil version of himself! (Yami Marik)
Season 3
Um... well, I dunno, but actually TV.com breaks up the Battle City arc into two seasons, so technically it is both season 2 and 3. I guess. It's hard to say, with anime, when it gets brought to America. But whatever. I'll go along with what TV.com says. So, season 3 starts with everyone heading for the Battle City finals, but they get redirected by a boy named Noah Kaiba. He was the son of Gozaburo Kaiba, the man who had adopted Seto and Mokuba. His mind had been preserved in a virtual world, and he wanted revenge against Seto for having been given control of KaibaCorp, instead of him. So Noah traps everyone in his virtual world, and there's rather a long story arc where they all have to have a bunch of duels before they can finally find their way back into the real world. That takes up about half the season, and it's followed by the Battle City finals, which comprise the rest of season 3. Eventually Yugi wins, Marik's good self is restored, Yami Marik is banished to the Shadow Realm, and the world is saved, and stuff. Around this time is when a sort of unofficial Yu-Gi-Oh! movie, Pyramid of Light, is set.
Season 4
But of course, season 4 presents an even greater threat. It turns out Duel Monsters are even older than ancient Egypt, they actually were around back in Atlantean days (10,000 years ago), and there's this parallel universe where all the Duel Monsters are real, and some bad guys, led by someone called Dartz, want to resurrect a powerful monster, Leviathan, to destroy the world and start it over from scratch, because they think they're good guys and humanity is evil. Meanwhile there are all these real monsters appearing and wreaking havoc in our world, and the bad guys steal the god cards, and there are these 3 dragons in the parallel world which each have to be awakened by someone. One is awakened by Yugi, one by Kaiba, and the third by Joey. Dartz's gang have cards of something called the Seal of Orichalcos, which traps two duelists in a ring during the duel, and at the end, whoever loses, loses his soul. Which Dartz intends to feed to Leviathan, to awaken it. The soul he wants most is the Pharaoh's. But of course he loses in the end.
Season 5
This season starts out peacefully enough, when Kaiba opens KaibaLand, a chain of theme parks which he was talking about in the prior season. And to publicize the grand opening, he holds another Duel Monsters tournament, the KaibaCorp Grand Championship. We see some familiar characters and a few new ones. Well, that arc lasts for awhile before a new adventure begins. I've missed some bits of the season, but what I can say is that at some point, the Pharaoh returns to his own time (and his own body), though he still has no memories. He's followed by Yami Bakura, who wants to reawaken Zorc, an evil god who the Pharaoh had defeated... but now, reliving these events without his memories, he should be unable to do so this time. Zorc could basically allow the Shadow Realm to consume the entire world, which would mean the future would never even happen! The Pharaoh is not alone, however. There are too many characters for me to remember, but like, each Millennium Item was controlled by one of six priests who were close to the Pharaoh (who had the Millennium Puzzle himself, of course), including one named Seto, and one named Isis (of whom Ishizu was the reincarnation). And there were plenty of others on his side besides the keepers of the Items. One was a girl named Mana, an old friend of the Pharaoh's and an apprentice sorceress or whatever. One was a vizier named Shimon Muran (of whom Solomon was the reincarnation). Also, his friends from the present travel to the past to search for his true name, which will unlock the rest of his memories and allow him to defeat Zorc.
Welp, of course they learn his name, and help him out, and Zorc is defeated. I'm not going to tell you his name, though. It's easy to find it online, if you want to. It doesn't really matter, of course, but you might as well watch the series to find out, if you're interested. Anyway, once the evil is defeated, the Pharaoh and Yugi and his friends return to the present, and Yugi and the Pharaoh must have one final duel against each other. If Yugi wins, the Pharaoh's soul will at last be able to find rest, though it's all very emotional for the whole gang, who'll be sorry to see the Pharaoh go, knowing they'll never get to see him again. On the other hand, if Yugi loses, the Pharaoh's spirit will remain trapped in this world. Won't tell you who wins that duel, but I think it's easy enough to guess. Well... I guess I can't think of anything else to say. It's hard to believe the series is finally over....
But before we go, I feel I would be remiss if I didn't mention some of the characters' favorite cards. Yugi's is the Dark Magician (though I prefer another of his cards, Dark Magician Girl... for reasons). Kaiba's is Blue Eyes White Dragon. Joey's is Red Eyes Black Dragon. Mai's is Harpy Lady. And... I guess that's all I can think of right now....
There's also a spinoff series called Yu-Gi-Oh! GX, which is set in the future, perhaps ten years or so. And one called Yu-Gi-Oh! Capsule Monsters, which is set within season 5 of the original series, but which I think is sort of unofficial, like the movie. And there are a few other spinoff series that I've never seen.