Some anime series that have been praised for their realistic depiction of everyday life include "March Comes in Like a Lion" (3-gatsu no Lion), "Silver Spoon" (Gin no Saji), "Barakamon," "Honey and Clover" (Hachimitsu to Clover), and "Sangatsu no Lion." These shows are known for their relatable characters, everyday struggles, and authentic portrayal of daily life.