Mushishi Zoku Shou

Both of them are episodic anime. Both of the stories are based on supernatural events and spirits.  

Relaxing peaceful feel, slow running, calm pace, disposition that is supported by excellent music opening and ending themes and a unique animation style. Both stories possess a mysterious feel to it and how it all comes together slowly but surely. 

Both of these are short storys that focus on the time we spend vs the destination. Both make you feel something.  

Both have traveling protagonists that are involved with people in a wholesome way. Both are: -chill pace -travelling protagonist -have good story (just look at the scores one these two) Mushishi is a bit better suited for a more mature audience. 

Both are episodic anime about a traveling protagonist who helps people deal with their supernatural encounters. Mononoke is much darker and more horrific than Mushishi. Mononoke runs in multiple episode story arcs unlike Mushishi.  

If periphrase popular song: "All you need is art". The art is the main character and the main motivation of these animes. Simple yet pretty backgrounds of Japan will help you relax and rest your mind during watching. Simple character design and pastel colours will only help with that. Lack of good protagonist make both shows calm, peaceful if not to say sleepy. You won't find here any moral or logical dilemmas (well, there are some in Robotic;Notes, but in a vegetative state). Primitive plot (if you consider there is any) is just linking together different landscapes brought to you by animators. All episodes are accompanied by nice meditative music themes. read more 

These series have a lot in common: - Both slow paced stories - Very beautiful surroundings, beautifully drawn - Supernatural themed - Good storylines