If you like the "Slice of Life" genre, then I would suggest an anime called Clannad. The execution of this anime is perfect! The characters are lovable, making you want to root for their goals, the music is top notch, the voice acting for dub and sub is really good, and the story is relatable.
My friends, this anime is the essence of beauty. It will make you shed a tear or two. By the end of this series, you will be in love!
I have some honorable mentions for this genre as well.
Golden Time-Great theme songs, breaks the High school setting cliche, but does feature some annoying characters (Main Character included), and at times im sure you will want to shout at your screen for how winey these characters are!
Another-More horror oriented, this anime has some pretty brutal scenes, but at the same time, it makes you want to learn it's dark secrets. The characters are great, the story is great, and the ending will throw you for a loop.
Ghost Maiden of Amnesia-A paranormal slice of life, revolving around ghost hunting club. The concept was great, the feels are there, but the ending just kind of steps on your feels.
Going for something more death note oriented,
The Future Diaries-Oh my god, this anime....I can't describe it! It just so.....