Zoids: Chaotic Century, TBS
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There are actually several Zoids series (based on several lines of toys), all of which take place on a planet called Zi. The first two series are collectively known (unofficially, I suppose) as "Classic Zoids," and this is the first of those two series. The later series aren't directly related to the first two series, but in all Zoids series, people pilot different types of mechas (which I think are sort of alive, but that was never entirely clear to me) called... zoids.
The first series is about a kid named Van Flyheit, who has a type of zoid called a Shield Liger (which later evolves into a Blade Liger). He meets a mysterious girl who has no memories. Van calls her Fiona, but later she'll remember her real name, as well as some more surprising and important facts about herself. I missed the first episode, but I guess he met her shortly after he found a capsule from which was born a small (roughly man-sized), silver, tyrannosaurish zoid he calls Zeke, who turns out to be something called an organoid, which means he can fuse with a full-sized zoid to increase its power (I also think organoids are more clearly alive than the mechas). Anyway, I guess Fiona hatched from a capsule like Zeke, or something.
There's also a zoid pilot named Irvine who has a Command Wolf. He wants to steal Zeke from Van, though they always seem to end up fighting together against some common enemy. They're later joined by an older girl named Moonbay. She has her own sort of zoid called a Gustav, and always sings her little song about how she's "a transporter of the wasteland."
There's a war going on between the Guylos Empire and the Helic Republic, who the Imperials consider just rebels. Meanwhile, Van and his new friends are searching for something called Zoid Eve, which Fiona has remembered the name of, but which no one knows anything about or has even ever heard of. But they keep getting caught up in the war, despite their best efforts to avoid it, first in Republican territory, later in Imperial territory. Eventually Emperor Zeppelin II dies, and his grandson, crown prince Rudolf ends the war. But then an Imperial lord named Prozen secretly tries to have Rudolf assassinated, so that he could take over the Empire. Van and his friends end up saving Rudolf and protecting him against Prozen's conspiracy. There are also a couple of desert pirates or something like that, Rosso and Viola, whose gang got busted up at one point, but the two of them show up sometimes in later eps to help protect Rudolf, though they used secret identities that could only possibly fool fictional characters.
There's also a character named Raven who has a Zaber Fang and a black organoid named Shadow, and they sometimes work for Prozen, but mainly Raven just follows his own agenda. He shows up to fight Van now and then. So anyway, Van and his friends' search for Zoid Eve gets sidetracked, but eventually fate leads them in directions they wanted to go, anyway. Or something. Because Prozen was looking for Zoid Eve himself, and other ancient zoids like the Death Saurer. And that's all I can really tell you for now, I don't even remember whether I ever got to see the end of the first series, but I'd definitely like to see the whole thing again sometime.
Zoids: Guardian Force
Depending on what source you consult, this may be considered either the second season of "Chaotic Century," or a separate series. Either way, it features the same characters and is set a few years later. After the war, the Empire and the Republic jointly established a peacekeeping task force called the Guardian Force, of which Van and Fiona are members. They're both certainly more grown up, now. Irvine and Moonbay are gone at first, but they show up later. And there's this guy Thomas Schubaltz who is also in the Guardian Force, who is the younger brother of an Imperial commander who was in the first series. He doesn't like Van much, but he's got a serious crush on Fiona. Thomas has a zoid called a DiBison, along with an A.I. computer system he created called Beek, which basically does the job of an organoid artificially. Beek sounds a lot like R2-D2.
Eventually Raven returns to make more trouble, and there's also a guy named Hiltz who has a red organoid named Ambient, and a woman named Reese who has a blue organoid named Specula. The three of them sometimes work as a team, and sometimes make trouble individually. Raven is now piloting a Geno Saurer, which eventually evolves into a Geno Breaker. And well, there were some more powerful zoids the Guardian Force would have to fight, but I missed the last several episodes. I definitely hope to see the whole thing sometime.
Then there's Zoids: New Century/Zero, and later there were a couple of series called "Zoids: Fuzors" and "Zoids: Genesis," but I haven't seen either of those series at all.