I want to provide information that will help readers make an informed decision about whether something I like is for them, without spoiling things. When links to further information / music / trailer(s) is given, this is just in case the reader wants it; a lot of the time it is a good idea to go into things knowing as little as possible.
The recommendations are provided in no particular order.
Genres are provided in order of most relevant to least.
For the anime entries, when it comes to subs vs dubs, I think that's mostly about personal opinion, but I'll state my opinion of the dub if I saw it.
Shin Sekai Yori is woefully underwatched. It's probably best to go into this with as little information as possible. The first episode does a good job of setting up the world for you, so I needn't explain it.
The music is really great and is strongly evocative [sample].
I would honestly state that this is my favourite anime.
A conspiracy theorist inventor who tries to act like a "mad scientist" stumbles upon a number of mysteries and a primitive form of time travel.
The characters are charming and the plot clever just as anything time travel related should be. Without an omnipotent plot device there is more of a sense of difficulty and danger for the characters than in other shows.
There's a fair number of references to anime/nerd culture due to the obsessions of the characters, which some viewers may not pick up on.
Some of the male protagonists aren't especially pleasant with some of the female characters. This will put some people off. However, it's presented as a character flaw, and the female characters are interesting and have more depth than your average anime / serial.
The dub is acceptable. The references it makes are more western. The main character's voice is better in the sub.
It's pronounced 'leed'. It's German for 'song', although in English it refers to a particular kind of German song.
As a warning: This is super gory and has lots of nudity. The nudity is always paired with gore for the sake of anti-fanservice. The first episode has more of it than any of the others iirc, but it's not the worst of it, and it was enough to put me off the series for years. It's not the focus of the show but it does feature in most episodes iirc.
In Elfen Lied some humans are born with telekinetic powers that are considered dangerous and as a result they are locked up in research facilities. The story isn't all action like the first episode might suggest, but it's about two ordinary people living with one of these mutants who's lost their memory.
Can't remember what the dub sounded like. I think it was fine.
An ace student finds a notebook that gives its user the power to kill anybody whose name is written in it.
The series focuses on the intellectual battle between ideologically opposed individuals trying to discover who each other another are.
The morality in the series is left open enough that one can watch whichever side they are on.
Dub is good.
The story is primarily about the fight between seven magic users, who are each in control of a magic resurrected historical or mythological figure. The prize for winning is a single wish. This might sound generic or whatever but there's a lot to the mages and heroes involved, who each have different motivations and conflicting personalities. The characters all get enough screen time that you can choose who you're rooting for. The art and fight scenes are excellent.
It's fairly dark a lot of the time, but in anime fashion it has light hearted scenes to balance it out.
The ending is actually spoiled by its own prequel which came out first and is less good. There are a few things that might be hard to understand at first because they expect the foreknowledge, but it's not needed.
It's a heterosexual romance slice of life, told from the boy's perspective, so it's probably more appealing to boys than girls. It gets emotional.
Dub is fine.
The series is set in an alternate history where World War Two hasn't happened, but three super-states control all of the world's land. Japan has just been annexed by Britannia (which consists mostly of the Americas, Britain is part of the European Union) and the natives are treated as second class citizens. A Britannian living in Japan forms an insurgency against the super-state authority, while a Japanese man becomes an honorary Britannian with the intent of making positive change from the inside.
There's plenty of light hearted aspects. It's not dark and gritty.
Dub is fine.
You need to know the following before you start watching: The episodes aren't presented in chronological order. The first episode is the most boring and won't make sense until during the second season. It's probably best to go into it knowing as little as possible. The film is very worth watching but only after the first season at the earliest.
It takes place in a high school, and I think that's significant enough that it'll only be fully appreciated by people that age.
Dub is good.
It's been a while since I watched so I can't remember how much information is given away at the start. You want less information going in to this anyway. There's some gore and an unsettling tone throughout. The colour composition is really interesting because they like to put yellow everywhere, which adds to the unsettling nature of what you're seeing because it's so unusual.
The soundtrack will give you the feeling for how creepy some of it is.
Series 1 didn't need a series 2, but more Utopia is great so no one complained. Series 2 finishes but naturally leaves a problem that series 3 needs to solve, which sadly isn't being made because Channel 4 wanted to air stuff that's newer. It's not really a problem imo, but I know some people won't watch stuff that's incomplete.
The story follows a depressed teenager who has to fight against giant monsters from space that threaten to end humanity. The show however is remembered for the psychological development of the characters dealing with the stresses of fighting monsters and teenage life. However it's much more intense than anything this sounds similar to. The world is futuristic and already fairly post apocalyptic, which adds to the hopelessness.
Dub is really bad in some places due to issues in production and not understanding the story. The film has inappropriate sound effects added with no respect for the material.
There's also a modern redo of the series as four films where the storyline diverges and follows a different possible turn of events. The final film hasn't come out yet. So far I'm enjoying it but I don't believe it's an equal alternative.