As per request by Walrus
(Why do you keep dragging me back?!), here's a list of anime you might enjoy. Note that I go for anime with good themes over anime that are just dumb action (like Sword Art Online, No Game No Life, Mirai Nikki... seriously, I feel like they're treating me as an idiot with those anime).
First up is
Fate/stay night: Unlimited Blade Works. It's about a boy that enters a magic ritual known as the Holy Grail War, where 7 masters summon 7 servants to fight for the Holy Grail. Every servant is based off of a myth or legends, and part of the war is figuring out the enemies identity and taking them out. Unlimited Blade Works is 1 out of 3 'routes', and so far the only animated one worth watching.
While that isn't the juiciest show in the franchise, it's the best introduction into the series so far. It's themes are mostly dealing with your ideals and coming to terms with it. After that, wait for the Heaven's Feel movies that will be coming out in 2017, where the theme of that "route" (as it's based off a visual novel) is picking between your ideals and reality.
After you finish Fate/stay night UBW and HF, you watch Fate/Zero. Fate/Zero is, like Fate/stay night, an all-out war, but it feels less focused on only 1 person, and more like you're watching the entire war, where a lot of different people with a lot of different ideals fight it out. As you can see, this show is very ideal-heavy. After that I'll give you a more light-hearted comedy, because Fate is kinda dark.
Next up I suggest pretty much any KyoAni show, but in particular
Nichijou, Hibike! Euphonium or
K-On!. Nichijou and K-On! are both comedy shows in a slice-of-life setting (especially K-On!), while Hibike! Euphonium is a Drama show about a music club that wants to play for a competition, but not everyone is willing to give it their all. All of them are a great watch, but if you for some reason absolutely hate moe anime (cutesy), then I suggest you stay away.
And next up as a final recommendation:
You can never go wrong with
Durarara!!. This anime is about "perspective". For the majority of the first season and also at times in the 2nd season, the entire episode will focus on 1 event. It will start by showing the aftermath from 1 perspective, and then proceeds to show you how it got to that point from another perspective (and sometimes even multiple at once!). Durarara!! is an intriguing show with a mystery vibe, and requires you to think a bit to solve the puzzle of how it got so far.
The first 10 episodes are a bit slow, but if you manage to sit through that, you'll be greeted by a lot of really well-done plottwists, interesting character dynamics and ofcourse, the 2nd Opening and its greatness.
EDIT: For good measure, here are also the Opening Themes for every show, to give you a good idea of atmosphere.
If you need any more recommendations at any given time, feel free to add me on Steam. I was once known as the Anime God here like 2 years ago, after all.
Click here to add me!