It's Rumiko Takahashi's fifth major manga series, after Urusei Yatsura, Maison Ikkoku, Ranma 1/2 and Inuyasha. Takahashi is the best-selling female comics artist in history, while all four of those series I've cited were hugely successful and ran for years. Having watched the anime of all four of those and being something of a Takahashi fan, I picked up the first six volumes of Rinne to check it out.
In short, it starts out a little dry, but its ideas are interesting and she's building up a lively cast of characters.
Rinne Rokudo is a part-shinigami, i.e. one of many Japanese incarnations of Death. His grandmother (Tamako) is a full shinigami and also a bit of an airhead, while his late grandfather was a human that Tamako fell in love with and gave an extra fifty years of life. Rinne is thus capable of living in the human world, but also has shinigami magic powers and works as one, helping lingering spirits to come to terms with their unresolved issues and move on to the next stage of reincarnation.
Sakura Mamiya is a human girl who can see ghosts and other spiritual beings, including Rinne even in shinigami mode.
...and that's the initial set-up. To be honest, at first I wasn't blown away. Both Rinne and Sakura are level-headed and don't do comedic overreactions, which is refreshing in anime heroes (especially from Takahashi) but for a while made them seem a little bloodless. Sakura in particular has ice in her veins. She won't even blink if confronted by things that would make you or me faint. She never gets angry. She never loses her cool. A story with only Rinne and Sakura in it will be the story of two efficient people doing the sensible thing at all times.
Admittedly there's the rest of Rinne's world to spice things up. Oh, and Sakura's connection with life might perhaps be weak, as is demonstrated in mildly disturbing fashion when she visits the land of the dead. However it's the supporting cast that liven things up and by contrast make Rinne and Sakura's self-possession look delicious.
Takahashi introduces them gradually. There's Rokumon, the old-fashioned demon cat. There's Tsubasa, the human exorcist who fancies Sakura and is a bit of an easily shocked stick-in-the-mud. There's Ageha, the female shinigami who fancies Rinne and generally causes trouble through her stupidity.
And those are Rinne's allies, or at least the best he's going to get. His enemies include devils, debtors and above all his funny but horrendous father, Sabato. Takahashi has a gift for appalling idiots and airheads and she's produced a prize specimen here. Sabato is a babe magnet with an endless supply of empty-headed charm and zero morals. If you see him with your sister, shoot to kill. He'd steal his son's furniture and forge his legal sign on debt guarantee documents for the sake of ready cash. He'd set up a company to usher humans prematurely into the next world for profit. Murder, in other words. We see his employees doing this to children. Admittedly it's all part of the circle of reincarnation and so this isn't as evil as it would be in a more real-world series, but there's still, at least, an ethical gap.
Let me put it this way. If you had to choose between Sabato as a father and Tatewaki Kuno from Ranma 1/2, you'd choose Tatewaki. Sabato's nowhere near as deranged or immediately annoying, but... no. Just no. Nothing good happens when he's around and it's his fault that Rinne's as poor as a church mouse. This is Rinne's main character trait. He has no money. At all. I wouldn't go so far as to call him mean, but he's raised tight-fistedness to the level of a martial art and he can weep tears of blood at the idea of waste. (I'm not exaggerating. We see it.)
Put all this together and you've got a pretty cool set-up. Rinne's poverty, ruthlessness and utter lack of sentiment are refreshing qualities in a hero, although compared to Sakura he's a drama queen. We also have the lingering spirits that they help, all of whom have an unresolved emotional issue that needs identifying and addressing. Sometimes this is moving, but it's just as likely to be funny. Takahashi's ghosts can be as petty, vain and shallow as anyone else, which makes for amusing ghost stories.
As for the art, it's what you'd expect from Takahashi. After all these years, she's got it down to a fine art. It's simple, but it's clean, funny and capable of expressive subtleties of body language. The only oddity I noticed is that the female regulars (Sakura, Ageha) will often be hanging in mid-air in flapping, super-short Japanese schoolgirl skirts. (Shinigami can fly.) The girls can't be unaware that they're showing their knickers. Takahashi never turns this into panty shots, thank goodness, and indeed is pretending to be unaware that any such thing could exist, but surely the other characters would have noticed?
One other thing I noticed is that Takahashi usually ties up her story arcs at the end of any given tankobon volume. The next volume will start a new arc. That's rather nice. I appreciated it. It's not an infallible rule (e.g. volumes 1 and 4), but note that the ghost samurai arc would have tied up neatly in the expected way had volume 1 not been only eight chapters long instead of the usual ten.
There's also an anime adaptation coming in April 2015 from Brain's Base, in case you needed further persuasion. Brain's Base are gods upon this earth. If they've chosen Rinne, then you should too.
Overall, I liked this. I'll be buying more next time I'm in Japan. It's still perfectly good in the early volumes, but it gets stronger and funnier as the supporting cast builds up. It let me admire Takahashi's knack for idiots. The "circle of reincarnation" subject matter makes it more dramatic than Takahashi's out-and-out comedies like Urusei Yatsura or Ranma 1/2, but it's lighter and funnier than Inu-Yasha. It's not dazzling, mind you. It's not reinventing the medium or anything. I wouldn't call it ground-breaking and it's not going to rock your world, but it's distinctive, characterful and funny.