Lost Shapes:
Un-Go, Neon Genesis Evangelion, and Anohana. They all represent fairly unique anime (Anohana less so than the others) and leave a lasting impact on the attentive viewer.
Note that with NGE, one must also watch the two films "Death and Rebirth" and "End of Evangelion" after the anime to complete the series.
SandStorm:
The animes I saw recently and loved were: DearS My little sister can't be this cute (both seasons) The world god only knows Dog Days and Dog Days Dash (I really LOVED this!) The hentai prince and the stone cat (it's not hentai don't worry, but is funny) Onegai Twins Haiyore! Nyaruko-san Ai Yori Aoshi
And from animes I saw a really, really long time ago, I'll never forget D'Grey man and Galaxy angels
I think I haven't forgotten any
veehive:
Anime, lately ... ummm ... I really haven't found anything that catches my eye for long. Looking forward to the 3rd season of Working!! (Wagnaria!! here in the USA) and will check the newly-announced anime of Kyoukai no Rin-ne when each appear in 2015. I'm doing more reading lately, and I recommend Monster Musume (VERY ecchi), Doctor Hitomi's Infirmary (somewhat ecchi), and BokuGirl (slightly ecchi).
Lost Shapes:
If you want a relatively mature storyline, good English dubbing, and amazing art, Gankutsuou: The Count of Monte Cristo is also suggested
RunningAway:
I recommend watching Kyoukai no Rinne