For anime, usually slice of life ones are good watch as they are most likely relaxing
Gakkou Gurashi
Baka to Test to Shoukanjuu
Shinryaku! Ika Musume
Crayon Shin Chan
Tonari no Kyuuketsuki-san
Himouto! Umaru-chan
Joukamachi no Dandelion
New Game!
Non-Non Biyori
Nijigasaki Gakuen School Idol Doukoukai/Love Live series
Idolmaster series
Beelzebub
Grand Blue (manga really recommended)
Gabriel DropOut
Kobayashi-san Chi no Maid Dragon
K-ON
Bofuri
Machikado Mazoku
City Hunter (action)
Tensura Nikki
For the plot-focused ones,
Kami Nomi zo Shiru Sekai
Tensei Shitara Slime Datta Ken
OreGairu
No Game No Life
Toji no Miko (really cool fighting animation)
JoJo series
For cartoons,
Tom and Jerry
The Simpsons
Oggy and The Cockroaches