If you like watching feels anime then I recommend:
Ano Hana - Jinta Yadomi and his group of childhood friends have become estranged after a tragic accident split them apart. Now in their high school years, a sudden surprise forces each of them to confront their guilt over what happened that day and come to terms with the ghosts of their past.
If you want something more on about action: (my personal favorite of all time)
Ansatsu Kyoushitsu & Season 2 - A humorous and action-packed story about a class of misfits who are trying to kill their new teacher ā an alien octopus with bizarre powers and super strength! The teacher has just destroyed the moon and is threatening to destroy the earth ā unless his students can destroy him first. What makes things more complicated is that heās the best teacher theyāve ever had!
If you want an anime that will make you feel depressed after watching it (pretty old but gold 
)
Death Note - Yagami Light is a 17-year-old genius from Japan who is tired of his life, school, and the state of the world as he knows it. One day, on the way home from class, Light stumbles upon a dark notebook with āDeath Noteā written on the front. Intrigued by its appearance, Light reads the first few sentences, only to find out that it states that anyone whose name is written inside will die. Discarding it as a joke, Light continues his daily activities. Soon after though, his human curiosity takes the better of him and prompts Light to try the notebook, discovering the truth behind first sentence. Now, with power in his hands, Yagami Light is on a quest to change the world and become God of the New World. His path to holy status wonāt be easy however, as another genius, known as L, is working against Lightās beliefs and Light himself. Who will win this power of Gods between humans?
*links and description taken from kissanime.to
