Well, as the topic title briefly states, I was wondering what the most unique premise for an anime or manga you’ve encountered was, in your opinion. I’ve been pondering this lately, I suppose mostly because I recently finished seeing all ten episodes of the Black Jack OVA. I found the premise of a mercenary-like unlicensed doctor to be fascinating (although I think the execution of the idea could have been handled a little bit better). What are all your thoughts on this?
If you may like Blackjack, then you should read or watch Ray. Ray was reminding of female Blackjack.
Hmmm… interesting topic… While I like a number of anime/manga, its kinda hard for me to exactly point out the titles that are UNIQUE, because most of them get cloned and/or fall into the cliche story lines. They also tend to “dip” into other genre. Ah! My Goddess is a perfect example of all these failings.
Ashita no Joe - anime/manga that are based entirely on a sport aren’t all that common (compared to harems and martial arts). However Ashita no Joe sets the standard for all these “sport titles” because its so damn good. The ending is also completely unexpected, but absolutely perfect.
Astroboy - seriously, do I need to really explain it? Astroboy pawns all. Megaman is a direct ripoff of him. Anime androids like Chobits steal inspiration from him. And yet while they copy Astroboy, they never quite seem to capture the SPIRIT of him.
Bari Bari Densetsu - before Initial D there was this, and it started the “motorsport genre” for the industry.
Gunslinger Girl - the entire setting and drama is unique, to the point of being disturbing. Each character has a crazy psyche, that when you THINK you know what its like, suddenly surprises you (Triela and Jean especially). Each of the girls is living a death sentence, yet their handers are even more tragic, in that the hardships of their past has forced them into accepting this kind of assignment. I have no idea how it’s gonna end either… its too original for something like that.
Hikaru no Go - they made a series out of Go. BORING ASS GO! Now that is awesome. I even learned the basic mechanics of Go thanks to this. Even more awesome? The games portrayed in the story, are real (i.e. a real Go Master helped the author).
Actually, the concept in itself was already present in Besson’s Nikita.
You’re absolutely right of course. I loved Nikita. Also GSG has already been avowed as being inspired by The Professional (aka LÈon). 
However the topic is: “most unique premise you’ve seen for an anime or manga?” Stressing those last two.
After all, if we were to go into outside media as sources, even the much acclaimed Astroboy is only an I, Robot rip. 
Of course, you know that Besson produced Nikita before he produced LÈon and said the latter was the former with the ideas and concepts refined?
I think this example you gave here best exemplifies the spirit of this thread.
What makes Black Jack so unique in my mind isn’t that it’s he’s a doctor. After all you can see plenty of medical TV programs. It’s that he’s an unlicensed, mercenary-like doctor.
Sayonara Zetsubou Sensei - a series that centralizes around dysfunctional personalities. The anime is random to the point of insanity. Kiri Komori is love and perfection.
Kinda neat how a suicidal teacher (actually an emo who just wants attention), has 32 dysfunctional students, and gives them a reason to live normal lives by becoming a central role model for them.
ooh good one Narg SZS is win . It may sound wierd but I’ll say Negima. I never encountered a mix of harem+romance+school drama+mahou @#*=¬Ä$ + shonen fighting journey . May not be completly harmonious but it blends well enough I say.
Let’s see, I liked the idea and setting of the Death Note manga it was different and I enjoyed it fo it; for anime Nodame Cantabile was quite unique plus it gives a glance of classical music to the youngsters 
Any of Satoshi Kon works fits the bill too, simply because the man is a genius 8)
I’ll raise you with Akagi, who knew Mahjong could be so engaging?
Zegapain: Through the first disc of the series, it totally feels like every other sci-fi / mecha anime you’ve ever seen. In fact, the first episode is about as underwhelming as any I’ve seen in a while. I almost didn’t make it to the second disc.
Once you find out what’s really happening, though, it’s a little mindblowing. Not going to spoil anything for anyone, but the questions raised by the situation the characters are in produces some very interesting existential questions. I’m curious to see how it will finish up.
I thought the concept behind Haibane Renmei is amongst the more unique stories and settings I’ve seen in anime. Actually, a lot of stuff that Yoshitoshi ABe has worked on seems to be pretty unique stuff (S.E. Lain, Haibane Renmei, Neia_7, etc.).
I’d vote for anything by Go Nagai: Devil Man and Devil Lady, Cutie Honey and Kekkoo Kamen, of course (Isn’t Black Jack one of his, too). Digging a little furthur back in the old memory banks: Doomed Megapolis (which links the Great Kanto Earthquake of 1923 to an incestous brother and sister and an evil wizard who is the ghost of all the Japanese soldiers who died in the Russo-Japanese War). Ghost in the Shell (wherein the difference between humans and machines is fast becoming undetectable) And a few others, but my vote for the most striking premise is from a pair of OAVs: St Michael’s Academy and Sins of the Sisters. One is the sequel to the other, but I’ve never been able to figure out which was which. But the story starts with Michael, a fourteenth century French boy, the leader of a Children’s Crusuade, who drowns himself rather than being sold into slavery by the Venetians. As he dies, he curses God and is reincarnated as a futanari in a Catholic girl’s school in modern-day Japan where the girls are being oppressed by the nuns. She rallys the girls and they set out to destroy ALL religion. There’s also a side story about the Headmistress of the school who is having an incestous affair with her brother, a Naval pilot frown WWII who visits her thru a time portal behind the altar in the school’s church. Together, these two are plotting to sell the the girls to the Japanese Army as comfort women. It’s from these simple elements that a pretty derl tootin’ anime is created.