Wagaya no Oinari-sama., Natsume Yuujinchou Recommendations
both involve youkai's, and have a similar feeling, except natsume yuujinchou is not as lighthearted as oinari sama.
Both has a male main character who finds a spiritual creature (in wagaya a fox and in Natsume a cat) that end up protecting them.. they also share that both creature know a person related to the male main character, who is also had a spiritual power..
So they are pretty much the same..
The main characters in both Anime inherit something from their grandmother. Thus their slice-of-life ends up adding a supernatural element to the whole matter.
I'll mostly be reiterating what has already been said: They both deal with a young man/boy who has a haughty guardian and they both must contend with youkai who pursue the main character(s). They both also have episodes that deal with helping youkai and Shinto gods in solving problems. Somehow, I just get a somewhat similar feeling when watching Natsume as when I watched Oinari. On the other hand, as others have said, Wagaya is more light-hearted and less melancholy/nostalgic than Natsume. It's been a year and a half since I watched Oinari so I may be remembering certain details incorrectly. Anyway, if you've watched
In both series, there's that mystical feeling. Along with that, the main male protagonist meets an entity who is not so normal and displays supernatural powers.
There is of course the case of supernatural themes involved in both series dealing with various strange incidents and the creatures involved.
Both series also features somewhat of an episodic sequence that often incorporates what the main characters face in their every day lives.