I have not watched the original series but I enjoyed tenchi muyo: war on geminar a lot more than I should have. There is a lot of fan service, but what I loved about it was the incredibly overpowered MC Kenshi. If your not a fan of barely developed Gary sue characters then this is probably not for you, but watching stupidly awesome characters kicking ass and taking names is a guilty pleasure of mine.
The original OVA series was decent. The spin-offs, not so much. Except War on Geminar, which imo, is probably the best of the series.
I don't believe any of them have a conclusive romance choosing, but it's been eons since I've watched the spin-offs.
TENCHIIII!!!! This was one of my favorite series from the old Toonami days and introduced me to harems. The first 2 original OVA seasons are good while the last is a bit incoherent at times (I'm still a fan youth). The best overall series is Tenchi Universe which has the most continuous and coherent 26 episode storyline, and, most importantly, plenty of Kiyone. War on Geminar is the best spinoff and is probably better in quality than all of the original series. It's a definite watch in my book.
The original OVAs and Tenchi Universe are great. War on Geminar / Isekai no Seikishi Monogatari is garbage.
Well, y'know, what's a fanbase without unhelpfully conflicting opinions? ;)
But it seems I can be the first to actually answer your main question:
dakotasapphire said: Does it come to some sort of conclusion with the romance or does it stay as a harem?
There are several different alternate universes or timelines, which means each can have a different conclusion. Unfortunately for me, I've never been happy with any of their endings, and nowadays I'm more keen on shoujo romance than Tenchi... anyway, your guide:
Ends with what to me felt like an out-of-the-blue victor. It's okay, I guess, but it felt wrong when I was 12 and still does now that I'm almost 29. On the other hand I loved the dub's accompanying cheeseball song "Dimension of Love" then, and still love it now.
I do know one female fan of Tenchi Universe (I'm not sure about the other series) in real life. She says she likes it "because it's hilarious," just like why I enjoyed Ouran Koukou Host Club. On the other hand I don't think I've ever seen a girl-harem anime of "serious" quality equivalent to, say, Fruits Basket. Well, Clannad is technically a harem, but it doesn't really get good until it stops being one.
The top review spoils who the victor is, but that's fine because she actually seems at least somewhat comparable to a shoujo audience-insert girl. I hated the show when I saw it for the same reasons the reviewer describes, but their take on it makes me think again. Maybe I'll appreciate it more when I rewatch it.
The spinoff Tenchi Muyo! GXP has a "conclusive ending," but not the kind you'd want:
The MC marries ALL of the girls!
EDIT: I should add, my favorite thing about Tenchi (all three main series) is the worldbuilding and its living tech. Jurai and its tree-ships are majestic. Ryo-Ohki is a cute cabbit (cat-rabbit) who turns into a spaceship. No other anime has ever had an animal companion that turns into a spaceship, at least according to TV Tropes. See the Anime/Manga section here: http://tvtropes.org/pmwiki/pmwiki.php/Main/LivingShip