If you like the genres of supernatural, fantasy, comedy, or a bit of romance and slice-of-life, "Noragami" covers all five bases. It also features a decent soundtrack, wonderful animation style, and memorable characters. Before you get too excited, though, be warned that this series contains some major downsides, mostly in the story and character development.
It's difficult to explain without giving spoilers, but there were several elements of the plot and the Noragami world which ruffled my feathers and nearly ruined the series for me. The system of Gods and Weapons is flawed and unfair. The protagonist is a Narcissist posing as a moral authority. The development and closure for the character of Yuuki was, without giving spoilers, thoroughly disappointing. Many plot holes appear in this series as well. You can probably tell without hearing any spoilers that Noragami is not all it's cracked up to be.
That being said, I do think viewers should give this show a try; others may be less critical of the Gods' systems and less disappointed at the outcomes of the characters. One thing it really has going for it, too, is the humor of the series. In short, this one is hit-or-miss. You be like me: continually puzzled at the show's popularity, and thoroughly disappointed with the main characters. On the other hand you might fall in love with the characters, beautiful art, and comedic escapades. For me it only gets two and a half stars out of five.