Both involve people who have a "gift" that enables them to view spirits (not to mention not entirely friendly spiritual "guardians"). Natsume Yuujinchou seems to be a more shoujo variation on the themes of Selected Pandemonium, which is aimed squarely at an adult audience. Both are well worth a look if you like stories about the Japanese view of the supernatural.
Main character is a boy who can see spirits, an ability he inherited from his grandparent. Keeps his ability secret from others. He has an antagonistic relationship with his spirit-guardian. Helps and fights spirits depending on the situation.
These are probably the best two mature supernatural titles out there. Both have excellent artwork and engaging, if episodic, stories revolving around two men who have a "gift" that gives them a view into unique and mysterious worlds unseen by most people.