 If you liked
Mushishi
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 ...then you might like
Zoku Natsume Yuujinchou
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While the first season of Natsume Yuujinchou was already compared often to Mushishi, Natsume Yuujinchou was always a lot more gentler and less that's-the-way-life-is than Mushishi. Zoku Natsume Yuujinchou for the most part is just like the first series, but it's a tad bit darker and closer to Mushishi, with its theme being confronting with reality and making a choice rather than the changing of the main character of the first season. Otherwise, watch both series for the reasons stated by others for natsume Yuujichou.
(Zoku) Natsume Yuujincho and Mushishi both share that gentle pacing, along with being for the most part episodic (in a positive way), and a similar main character (though Ginko would be a 10 years older and more mature Natsume, if that's even possible). While Natsume Yuujincho deals with ayakashi and Mushishi with a most basic type of lifeform called mushi, you will likely find something in both that will tug at your heartstrings.