Tenchi Muyo Franchise Overview
The fan-favorite Tenchi Muyo franchise is a sprawling mess of unrelated continuities; we break it down to relieve some of the confusion.
Tenchi Muyo, an original anime series created by Pioneer in the mid '90s, is one of the original fan-favorite megaseries. Its wacky stories, hilarious situations, lots of violent-but-pretty girls, and a slightly off-kilter sense of humor endeared fans to the series from the first episode of the OVAs that started the whole mess. And it is a mess, consisting of about five entirely different continuities involving the same basic set of characters.
The title, incidentally, is a multi-layered pun, but in Japanese is mainly recognizable as a common label on boxes, meaning "This End Up."
Tenchi Muyo is the ongoing story of Tenchi Masaki. Tenchi is one of those anime guys that has more luck with the ladies than anybody deserves. Well, luck might not quite be the word... he ends up living with two violent arch-rivals for his affections, Princess Ayeka and former space pirate Ryoko, along with a whole slew of other women and his father and grandfather. These folks also have a tendency to attract intergalactic villains. Quiet, his life is not.
Of course, the details of the story and backstory depend quite a bit on which continuity you're looking at, but the basic setup is more or less the same across all of them except the Pretty Sammy spin-off.
Or, more accurately, complete lack of continuity. As mentioned, there are between three and five entirely separate continuities, depending on how you count.
OVA (aka "Ryou-Ohki")
The original is the "Ryou-Ohki" continuity, more commonly known as the OVA continuity. It mainly consists of the three Ryou-Ohki OVA series (two "original" ones and one new one, produced about a decade later). The Mihoshi Special is a loosely-related a side-story, but usually included as part of the OVA continuity.
More peripherally related are the is the GXP TV series. Although GXP follows a completely unrelated Tenchi-lookalike earth kid who joins the Galaxy Police, it does belong in the OVA continuity. (Interestingly, the third OVA series includes several things that are referenced in GXP, which is set later, even though GXP was produced first.) It also provides quite a bit of information about the Jurai royal family.
Even more peripherally related than that is the newer lengthy OVA series Tenchi Muyo! War on Geminar. While it is set in a completely different parallel universe and none of the original cast appears, the main character is Earthling-stuck-in-another-world Kenshi Masaki, Tenchi's 15-year-old half-brother; there are a few subtle in-jokes fans will pick up on.
In other media, the Tenchi Muyo manga series is also intended as a direct continuation of the story, though the third OVA series doesn't seem to pay any attention to it (incidentally, there's no difference between original and "new" manga series other than the title).
Finally, the second movie, Daughter of Darkness, almost belongs here; it is based on a series of novels that were intended as part of the OVA continuity, but the introduction of Kiyone (her first appearance was in the novels) and Mayuka were not carried through into the subsequent OVA series.
TV (aka "Universe")
The first two-season TV series is a retelling of roughly the same story as the early OVAs with slightly altered characters, new villains, and--unlike the OVAs--a definite end.
The first and third movies almost fit in the TV continuity, but not quite, putting them in their own "movie" continuity. The backstory in the first, Tenchi Muyo In Love, is roughly the same as the TV series, and it could fit. The third movie, Tenchi Muyo In Love 2, is intended to follow the first movie but doesn't fit with the events of the TV continuity.
As noted above, the second movie is off on its own, trying to be in the OVA continuity.
Tenchi In Tokyo
Odd man out is the Tenchi In Tokyo (originally "New Tenchi Muyo") two-season TV series. It seems to pick up in the middle of the story and assumes some familiarity with the characters, but follows its own unique continuity, with totally different origins for all the characters explained in a later episode. This series chronicles Tenchi's adventures as a high school student in Tokyo with yet another pretty (and this time comparatively normal) girl, Sakuya, after him.
Off in left field are the Pretty Sammy spinoff series, which use use the same basic set of characters without the crazy backstories, and change Sasami into a Sailor Moon-style magical girl heroine. Sasami, a newer series, is attached to this spinoff franchise.
Where Do I Start
If you're starting cold, it's best to start your Tenchi obsession--and once you start, obsession it will likely become--at the beginning of either the first TV series ("Universe") or the OVAs. Those are the only two that don't assume you know who the characters are at the beginning.
That said, the OVA continuity is the One True Continuity, end of story. It's bigger, better, and far crazier than any of the others, even when you include ugly stepchildren like GXP. It's also the only one still going.
A brief character rundown.
The kind, level-headed high school student at the center of way too much attention. He lost his mother at a young age, and lives with his father and/or grandfather. Depending on which series you look at, he's either a relatively normal guy (by anime standards) stuck with some abnormal roommates, or an unknowing descendant of the Jurai royal family being trained as a swordsman and shrine-keeper by his grandfather. Regardless of the continuity, until the series starts he lived a relatively quiet life in the country.
Crown princess of the Jurai royal family, destined to become the future ruler of an interplanetary empire. Regardless of continuity, she's pretty, refined, and has a vicious temper, particularly when it comes to Ryoko. In the OVA continuity she is older than she looks, as are most of the Jurai royal family.
A mostly-reformed space pirate known for inflicting planetary-scale destruction in the process of raiding civilizations for their valuables. She's also got a faithful sidekick, Ryou-Ohki, a cute, furry little half rabbit/half cat that just happens to be able to turn into a very large, very powerful spaceship... that meows. (Actually, it "miyaa"s, but that's getting technical). Ryoko is willing to do just about anything to catch Tenchi's heart (or, failing that, his body). In the OVA continuity, considerably older than she looks.
Ayeka's cute, cheerful, slightly mischievous younger sister and best friend/perch of Ryo-ohki; she's younger than the rest of the group, and is the household cook.
A semi-mad scientist and the self-proclaimed greatest genius in the universe; currently inhabits a diminutive, young-seeming body. She spends most of her time in her lab--a vast complex located in a dimensional pocket, with a door under the stairs of Tenchi's house. In the OVA continuity, drastically older than she looks.
Mihoshi and Kiyone
Wayward Galaxy Police agents; Mihoshi has a nose for trouble and a brain for... not much. Kiyone is Mihoshi's considerably less ditzy partner. Kiyone was not a regular character in the OVA, though she was mentioned as Mihoshi's former partner and was first introduced properly in novels that were intended as part of the OVA continuity.
Tenchi's mother died while he was a boy, leaving him to be raised by his slightly-weird father, an architect. Tenchi was also partly raised by by his maternal grandfather (who happens to look a lot like his son-in-law, and in Japanese shares the same voice actor), who cares for the shrine that Tenchi will probably inherit (if someone doesn't accidentally kill him first). Tenchi's grandfather is known for keeping a lot of secrets.