Imagine you're God. Complete dominion over time and space, etc. However you're not immortal and you're going to die soon, which will cause universal destruction if you don't find a successor.
How would you choose your replacement? Well, this world's God (called Deus Ex Machina) starts with a shortlist of twelve people with emotional problems. One's a serial killer. Another's a terrorist. Another wants to destroy the world. Deus then sets them loose on each other in a murder competition, with the prize for the last survivor being godhood. This probably sounds mad. It is. Deus seems to be doing this partly for entertainment and indeed has tweaked things to help the bloodbath proceed nice and quickly. Oh, and in case it wasn't horrible enough already, one of the deathmatch contestants is a pre-school child.
Furthermore, to make things more interesting, everyone receives a Future Diary, containing all the entries they'll ever write and telling them when they're going to die. However the future isn't fixed. Diary entries will change if someone acts on this foreknowledge. What's more interesting is that a diary will only contain entries that its owner was going to have written, so for instance a police detective's diary will only mention the progress of his investigations, a fanatical dog breeder's diary will only mention his dogs, etc.
This is pretty extreme. More importantly, though, this series is also a love story between a nice boy who means well and an insane stalker who murders dozens of people on-screen.
First, though, a language lesson. Today we'll be learning the word "yandere".
There's a "dere" family of Japanese otaku words that can't easily be translated into English. By far the best-known is "tsundere", made from "tsun-tsun" (prickly, aloof) and "dere-dere" (lovestruck, fawning). Such characters can flip between one and the other, with a cold surface personality and a hidden loving side underneath. Anime and manga have hundreds of tsundere, which in fairness are merely exaggerating a not uncommon human trait.
(Incidentally, "dere-dere" doesn't just mean "lovey-dovey", as I think a lot of Western anime fans assume. It's not a positive word. Its other connotations can include slovenliness, laziness, flirting and philandering.)
Other "dere" words include "kuudere" (apparently cold) and "dandere" (apparently quiet and withdrawn). This family has an odd one out, though, which is yandere ("darkness + dere"). Unlike the others, yandere are dangerous. She  will have a One True Love to whom she's devoted. She'll do anything to be with him. Anything. Usually identifiable by her blank-eyed stare when murdering people she sees as obstacles.
 - most yandere are female.
Of all the yandere in anime, though, Future Diary's Yuno Gasai is their queen. She's their poster girl. Look it up on the internet and you'll see her picture. She's a rare and special thing, you see, a yandere protagonist. She's one of our heroes, despite being an axe-murderer and utterly without sanity. If something happens that she can't process, she'll edit her own memories and thereafter have no awareness of having met the person in question. She'll tell Yukiteru to sacrifice his friends as decoys, unable to comprehend that this might freak him out. Other girls talking to him is a Very Bad Idea. She wants to keep Yukiteru safe, but who's to say what "safe" means? How about drugging him, chaining him up in a basement and making him watch as she lays deathtraps for his friends? Yeah, that would count.
A walking nightmare? Oh yeah. Crazy awesome? You betcha. Yuno's insanity is one of this show's big selling points, although admittedly there are also people who don't share this opinion (to put it mildly).
In the world of Future Diary, you see, a Yuno is exactly what you need. She's clever, she's good at evaluating dangerous situations and she'll kill everyone in the room if that's what it takes to keep Yukiteru alive. A small child? Don't doubt it. She's terrifying, yes, but as it happens she's simply meeting extreme situations with appropriately extreme actions. She's the best thing that could have happened to Yukiteru, she's 100% on his side and all he needs to do is to get over the, um, more disconcerting sides of her personality. (Hint: not easy.) In some ways, this a gender-flipped version of conventional romance, with Yuno being the aggressive, physical one and Yukiteru being the nervous, timid one who'll need a lot of time to win over. It's also arguably a deconstruction of the male fantasy of "wouldn't it be dreamy if the hottest girl in school was crazy about you?" Ahahahahaha, no.
Besides, she really does love him. She can be gentle and vulnerable. She's still a fourteen-year-old girl, full of insecurity and even occasionally flashes of self-awareness. The Yukiteru-Yuno relationship can be heartwarming and sweet, until of course Yuno kills the mood by saying or doing something insane.
If I were Yukiteru, would I? Yes, I would. She's beautiful, sincere and even admirable in her unshakeability. Sanity is overrated. Treat her even a tenth as well as she'll treat you and you'll have the strongest relationship in the world. There might be the occasional incident, but you should be able to minimise the casualties if you remember that she'll do almost anything if you ask nicely. Just remember to watch her carefully, never speak to any other women as long as you live and never leave her alone with family members.
Time to return to Future Diary! I could discuss Yuno for hours, but there's lots more here too.
It's not a depressing show. It's insanely dark and blood-drenched, but I found it an entertaining kind of darkness. Pretty much everyone goes over the moral event horizon at some point (e.g. the orphanage), Yukiteru's mental stability is torn into bitty pieces and people go around murdering their friends. If you don't think that sounds like fun, avoid this show. However godlike powers are awaiting the winner and, yes, Yukiteru does ask if he'd be able to resurrect everyone he killed. The finale is a bizarre combination of (a) happy ending and (b) wrist-slittingly horrific and depressing... until a bit after the closing credits that's so weird and inexplicable that I had trouble accepting that it was meant to be objective reality.
Don't worry, it's true. It happens. (This makes me happy.) You can verify this either by buying the manga, reading its wikipedia summary or watching the 2013 OVA. The first ten minutes of the latter are fan-pleasing rubbish and a disgrace to the franchise, but after that we get the explanation of what happened that I'd have preferred to see in the show itself.
The other OVA is apparently just an eight-minute summary of the manga's beginning. Doesn't sound essential. There's also a live-action TV drama that wild horses couldn't make me watch, while what little I heard of the anime's English dub hurt my brain, but I'm thinking of buying the manga.
I imagine you already know whether you're going to like this or not. (Not everyone does, which is fine.) Fascinating cast, clever games of diary vs. diary mind chess and God being a bastard. That said, though, there's more to the series than just people fighting to the death. That would be thin. There's 26 episodes of strong plot. Diary owners befriend each other and make alliances. Not everyone even wants to be God. Above all, though, there's Yuno.
"If I kill you two, Yuki will look at me again!"