TENCHI MUYO! should be a hard series to like and even to define because it is a series plagued with reboots, semi-sequels, and peculiar OVA follow-ups (essentially these are Japanese releases that are straight to video animations rather than straight to TV).
The odd thing is that what is known as the first generation TENCHI MUYO! show is in fact an OVA itself. The first six episodes are what is collectively known as TENCHI MUYO! RYO-OHKI or just plain OVA 1 (although this title can also refer to all of the OVAs, too). This OVA 1 was released in Japan on September 25, 1992. I turned two years old that day.
Then that was it. Put a fork in it because the TENCHI MUYO! series is done.
Not really, though. The series caught on.
In 1994, a TENCHI MUYO! Special called The Night before the Carnival was released. Generally, this is included as part of the greater TENCHI MUYO! RYO-OHKI series even though it is really a spacer between what was known as OVA 1 and what would become OVA 2. There was also a TENCHI MUYO! MIHOSHI SPECIAL released, but I have yet to see that particular entry. FUNimation doesn't have it available for streaming and I don't believe it is available on DVD or blu-ray at the moment. Although I'm sure there are a few places where you (or I) can watch it for free or buy it at an overwhelmingly elevated price. At any rate, the Mihoshi special could only serve to confuse a few people because it takes place in the RYO-OHKI timeline but introduces a character that would later be in the alternate universe/timeline show TENCHI UNIVERSE.
TENCHI UNIVERSE is a retelling of RYO-OHKI OVA 1 and that series lasted for 26 episodes, concluding its run in 1995. Keep in mind that while TENCHI UNIVERSE finished its run in Japan in 1995, the third OVA in TENCHI MUYO! RYO-OHKI was eight years down the pipeline. The third OVA in TENCHI MUYO! RYO-OHKI has a different animation style than the first two OVAs of TENCHI MUYO! RYO-OHKI and the series TENCHI UNIVERSE. The spaceships also look very different, almost like an attempt to make it look like a computer game or something. Kind of hokey, really.
TENCHI IN TOKYO was another reboot that came about in 1997 while TENCHI MUYO! RYO-OHKI! still remained unfinished. The third OVA in RYO-OHKI did not come about until 2003. TENCHI IN TOKYO is generally considered the worst of the bunch, but it's been awhile since I've seen it so I can't support or counter that status just yet.
In 2002 yet another TENCHI-related series came out and this one was called TENCHI MUYO! GXP. GXP takes place in the RYO-OHKI timeline (a year after the final OVA in RYO-OHKI even though RYO-OHKI still remained unfinished at the time), but is not itself a sequel. In fact, the main characters are only given slight cameos because GXP follows different characters. So, while not a spinoff or a reboot, it is not the conclusion to RYO-OHKI.
When RYO-OHKI did recommence it did so with six more episodes and these final six episodes are called OVA 3. In 2005 a "special episode" of Tenchi Muyo! Ryo-Ohki called Final Confrontations was released and that is essentially the absolute final episode of the series unless something else happens in the future.
All in all, we have 20 episodes of TENCHI MUYO! RYO-OHKI! released over a span of thirteen years. That's a helluva wait. It still might not be done. Who knows?
There is another series called Tenchi Muyo! War on Geminar that was released in 2009 and this series takes place 15 years after GXP so it's technically part of the RYO-OHKI storyline, but it doesn't feature Tenchi or the other main characters much like GXP. This newer series follows Tenchi's half-brother Kenshi around.
Got all of that? Good. I'm not repeating it.
Now I'm going to talk about the series itself.
In case you haven't guessed, TENCHI MUYO! (regardless of which universe or alternate telling we are talking about) follows around boy named Tenchi Masaki as he goes through the trouble of everyday life of being the center of a harem. In RYO-OHKI, Tenchi accidently revives an old space pirate named Ryoko and that's when all hell breaks loose. Through happenstance and luck, Tenchi manages to keep from being killed by the pirate but he doesn't escape from her clutches. It seems that Ryoko has developed a sudden and rather intense crush on the young boy. And, in perfectly understandable fashion, she refuses to leave his home. The rest of the harem essentially follows that established pattern. Ayeka, Sasami, Washu, and Mihoshi all wind up with Tenchi through luck or misfortune and end up living with Tenchi and Tenchi's grandfather and with each other.
While this may sound like a typical harem anime, it really isn't. Tenchi doesn't accept any of the advances from the women because he prefers to keep the family unit intact rather than try to dissolve it by pursuing romance. He also isn't a complete idiot or wimp.
There's also the plot to consider. On one hand you could write it off as being just another thing to wade through as you wait for the boob or pantyshot of your favorite female character, but the plot is pretty complicated and intriguing. Each of the OVAs has a different main villain and a different storyline, but they all advance with each episode and by the time you reach the end of OVA 3 things will undoubtedly seem bizarre and confusing. Yeah, I know it's "just a harem anime," but they must've put a lot of thought into this or did some hard drugs or something because the solution to everything seems... Well, almost Lovecraftian. We have space people. We have trees and rabbits that control or are spaceships with superpowers. We have gods who seek to know if there's anything greater above them. Gods who are trees. Gods who are kids. Time travel. And carrots.
Then of course we have Tenchi and his harem thrown into all of this. Somehow Tenchi is at the center of all of this because he is the manifestation of what the gods were trying to accomplish. Something like that, anyway.
I watched this series in Japanese with English subtitles very recently, but all of the details seem pretty muddy. I'm not sure I like the final OVA as much as I like the first two, but it's a decent if not confusing conclusion.
TENCHI MUYO! RYO-OHKI is a classic anime show, though. At least the first two OVAs are. If you haven't seen them then you just aren't an anime fan. It's like claiming to be a music fan without having ever listened to classical music. If you don't know your roots then you just don't know anything.
This show is streaming on FUNimation with the first thirteen episodes being labeled as TENCHI MUYO! OVA SERIES and the final seven episodes being labeled as TENCHI MUYO! RYO-OHKI. Or you could buy them on Blu-ray/DVD from Amazon, but I believe they are also divided up in the same fashion.