On my fairly extensive anime list, I have about 12 series rated 10/10. Toaru Majutsu no Index being my favourite, Death Note, Fullmetal Alchemist: Brotherhood, Zetsuen no Tempest, Clannad, Steins;Gate, Haiyore! Nyaruko-San, Angel Beats! and a few others.
These series aren't exactly linked well to each other on the surface, but are all very well made with great characters, they also do the basics well, the music, the animation and artwork, after these things, its mainly personal preference (partly why some series appear on this list, while Attack on Titan and Sword Art Online do not).
Anime has a great quality of having such a vast range of genres and stories to choose from, there are no limits to the insanity of power levels (yes we all know they reach over 9,000), explosions, scale of size and everything you can think about. Because of this i refuse to believe there is a person out there who cannot relate to at least one series out there, those which I've listed are just an insight into the many which I've enjoyed.