i've been watching anime for half a decade and these are the ones i'd recommend: one piece, naruto, death note and attack on titan
firstly, are you interested in reading manga? because the mangas for some animes are a thousand times better than their anime adaptations. like 'one piece' for example. one piece is currently the best and most popular on going anime/manga to date. having watched both its anime and manga, i can confidently tell you that you would be doing yourself a disservice by watching the anime before reading the manga. if you want to truly enjoy one piece the way its author intended, you must read its manga. its currently on its 735th chapter and still maintaining its position as the best manga currently. the anime doesn't do it justice but if you still want to watch it, do so after reading the manga.
so yea, the first one i'm recommending is 'one piece' and you can start reading the manga here
http://www.mangareader.net/103-2039-4/one-piece/chapter-1.html don't let the art bother you. it's alot more refined now than it was at the start, so much so that one piece has become renowned for its artistic originality. oh, and the manga panels are meant to be read from right to left, in case you didn't know.
the next one i'd recommend is naruto. unlike one piece, the anime for naruto is amazing, so you'd get as much satisfaction watching it as you would reading it.
the next is: attack on titan. this anime is literally god. it literally makes me cry tears of
happiness epicness.
the last is: death note. just watch it.