I agree with a lot of the recommendations on this list and glad to see the anime love! Since you guys are doing a good job already, I will only recommend a couple of shows not already mentioned. I tried to pick from some diverse genres so that hopefully people can find something they like. If fancy strikes, I have some more shows that I think deserve a recommendation and that haven't been mentioned. I might come back and give them the same treatment, if fancy strikes.

[hider=Shin Sekai Yori]Shin Sekai Yori / From the New World

Forms of Media: Novel, Manga, Anime

Genres: Sci-fi, Supernatural, Horror, Drama

[img]http://vignette4.wikia.nocookie.net/shinsekaiyori/images/2/25/Wallpaper_04.jpg/revision/latest/scale-to-width-down/670?cb=20140414180025[/img]

It's hard to tell you a whole bunch about this one without falling into potential spoiler territory (even if those spoilers are revealed fairly early into the show). I found this show at once both fascinating and with greater depth then many shows I have come across (perhaps stemming from it's adaptation from a full length novel rather than a light novel). I can say for certainty that if you are interested in Post-apocalyptic sci-fi that isn't incredibly apparent at first glance, Creeping horror at the great lengths humanity can be stretched too, following a group of characters from youth to adulthood as they struggle with their place in the world, or just something a little different than what your standard anime will give you then this is 100% worth your time.

All that being said, some things to watch out for when viewing (I have only seen the anime, so that is what I will go off of here.) is that the pacing can sometimes be a little wanky/slow calling to mind things like Steins;Gate where it takes a bit to get where you want it to go. That being said, sometimes the pacing works wonders allowing the time skips to have greater impact as the show moves on. 

Considering it's already 2015 I don't believe it needs to be addressed all that much, but the show does show homoesexual relations (M/M and F/F) through out a good portion of it's run time and they feature an even greater presence in the novel and manga (Nothing Explicit, though things like that are implied). This is done rather tastefully promoting character growth and not really with the intent of fanservice (Tumblr loves the Yaoi gifs from this show, my girl-friend has made me fully aware, but the point does still stand.) If this is something that bothers/makes you uncomfortable when viewing with family or whatever no big deal, fair warning though.
[/hider]

[hider=Shirobako]Shirobako

Forms of Media: Anime

Genres: Slice-of-life, Comedy

[img]https://upload.wikimedia.org/wikipedia/en/8/81/Shirobako_Promotional_Poster.png[/img]

This anime original seemed almost a labor of love by P.A. Works and did rather well in it's 25 episode run. The show itself is an anime about the making of anime, as meta as that may be it makes for a very compelling show with a large colorful cast and genuinely humorous comedy. In typical anime fashion it starts by following five girls in their High school Animation club as they vow to one day work on an anime together. Unlike typical anime fashion, it quickly leaves the high school setting behind as each of the girls graduates to the workforce/college life and their aforementioned dream seeming just that, a dream.

If you are interested in a large/realistic cast of characters working together in interesting ways, an accurate look at the inner workings of the animation industry in japan and the hardships many different people inside it face, a surprisingly mature look at adults dealing with the struggles that come with their jobs, or a genuinely fun cast of characters then you will probably enjoy this anime.

Not a whole lot of complaints can be leveled at this one. Both the animation and pacing are pretty rock solid and the 25 episode format seems like the perfect length to tell the story they needed too. Within a few episodes you will probably be able to tell if this is the kind of show to interest you.[/hider]

[hider=Hyoka]Hyōka

Forms of Media: Light Novel, Manga, Anime

Genres: Mystery, Slice-of-life, Drama

[img]http://vignette3.wikia.nocookie.net/hyouka/images/7/7f/COVER.jpg/revision/latest?cb=20120501105619[/img]

Seeing quite a few mentions for other Kyoto Animation shows, I feel like Hyoka deserves a special mention. A incredibly well animated piece of work, I am convinced that It could be recommended on that fact alone. On top of this it comes along with a compelling arc structure revolving around each mystery that the group faces. Add on to this a compelling cast of characters which are all unique enough for you to bond with and show -actual- growth over the course of the entire anime's run time and you have a real star of a show.

I have already touched on it once, but it really does need to be stated how good the art in this show is. Specifically after the wide spread success of K-on! (Another really good show, but for different reasons) KyoAni found themselves with quite a bit of money to spend and this show certainly shows it. Something else interesting, this show was before the widespread use of CGI in scenes involving a large number of people so keep an eye out for scenes like walking to school etc.. and you will find the level of detail hand drawn in the background is really quite impressive.

I do have to give a caveat on this one. Despite the praise I have already given it, it just might not be your cup of tea. This show can move at what sometimes feels like a glacial pace, reminiscent of something like Mushishsi, and requires interest in the story to watch for binge sessions. These pacing problems vary depending on the specific arc, with some being near flawless (Festival) and others being less so. If you like the art style but the pacing just isn't cutting it for you, maybe try some of KyoAni's other shows Tamako Market and Hibike! Euphonium are to relatively recent shows that boast impressive art while having a shorter run time and a quicker pace.[/hider]

Full disclaimer: All of these shows are imperfect in some way and might not be your cup of tea. (Though this applies to literally everything, hah.) I also list that 2/3 of these shows have multiple forms of media to view them through, but I have only seen them in their animated form so my suggestion is for that form of consumption specifically.