Well, you came to the right place.
I happen to know some animes of phenomenal quality.
Honorable mention: Steins Gate. Never watched it myself so that's why it's not on the list. But I've heard it's great.
My Personal Top 10:
10. Senyuu - craziest thing ever
9. Danganropa - great murder mystery
8. Bleach - IK it's mainstream, but it's worth watching still.
7. Magii
6. Sword Art Online first arc (ALO not even worth your time tho) and maybe GGO
5. BRK/BRNK - Just well polished
4. World Trigger - make sure you give this a chance
3. Log Horizon - Makes you think and theorize. If you can survive the first 8 episodes it picks up so much that it overcompensates for a weak start so much that it gets a rank 3.
2. Welcome to the NHK - Worth mentioning what this one and #1 is about. This one is about a NEET/hikikimori leaving his apartment after total isolation for two years, with the help of anime's best waifu ever, Mizaki. Just know what you're getting into before you start it. It's an emotional rollercoaster. 9.8/10 - could have better animation but is ultra meaningful and has a great plot
1. Erased - Premise: This anime follows a 29 year old character named Satoru. He experiences strange phenomenas known as revivals. They basically allow him to travel back in time an average of five minutes beforehand, but he can't actually control or activate this power intentionally. It also only happens when someone dies. Satoru realizes this and is able to stop most of them. One day, a serial killer makes his move and Satoru is framed for his mother's death. Unable to escape, a revival is triggered that sends him back.... to his childhood, when there was a chain of killings.
Genre: Thriller, Drama, Mystery, a little Romance, Action
I think this is the best anime out there period. It's ongoing, going to wrap itself up supposedly as a 12 episode anime so it's doable, full of symbolism, makes you think, theorize, and feel, superb animation, catchy themes, and well polished. Nothing here will dissapoint.
10/10
