By Eri Takenashi. Released in Japan by Ichijinsha, serialization ongoing (but on hiatus) in the magazine Comic REX. Released in North America by Bandai.
I will admit, I did not get this manga for the plot or characters, so in that respect it's my own damn fault. I got it because I'd heard of its reputation. This is, among fandom here in the West, the first modern series that made people think "Wow, Japanese otaku are insane." (Note that this behavior has been quite consistent in the past, but the media coverage for the Kannagi incident was such that it was like seeing it again for the first time.) To be brief, the main character in the Kannagi manga/anime noted that she had a boyfriend before she met the hero, and fans freaked out, declaring that she was "second-hand goods" and a "slut". Leaving aside the sheer sexism of this, it was the over the top silliness that made it newsworthy, with the fans burning their manga in protest. (However, given these fans, I suspect they only burned one of the 3 copies they bought.) There was quite a furor in Japan, and in fact the author went on leave due to health reasons and has not returned.
So I wanted to get it to see if there was anything to make a fuss over, or if this is a classic case of making something out of nothing. Sadly, it turns out to be the latter here, as judging by Volume 1, at least, Kannagi is a very predictable title, a sort of Oh My Goddess for the moe crowd. The basic premise is that our "ordinary yet likeable" boy, Jin, has recently carved a statue of a goddess from the remains of a sacred tree that was cut down as they're consolidating shrines in the area. It's part of a school project, but complications ensue when a teenage girl breaks out of his statue and turns out to be the deity of the tree, Nagi. She's a little upset about the tree being gone, as you can imagine, and with Jin's help starts going around getting rid of the "impurities" that have risen up as a result.
I mentioned that it's similar to Oh My Goddess, which is true, but there's also a great deal of the visual novel/datesim quality to all of this. The color page in the front of the manga, in fact, is done up exactly as a datesim (except you actually see Jin's face, instead of a blank where you can put your own), as he sees Nagi and his childhood friend Tsugumi posing cutely at him. The actual plot, thankfully, is less romance oriented so far. We see Jin's school, which Nagi quickly transfers into, and meet the members of the Art Club he's in, who don't really get much to do this first volume except be goofy minor characters.
Honestly, very little happens at all. There's a bit of plot in the final chapter, where we meet a rival goddess who is also gathering believers and purifying, and there seems to be an underlying threat of Nagi fading away if she is forgotten (which, ironically, may become true in the REAL world if the manga never restarts in Japan). But overall, this feels so insubstantial that it's like reading nothing at all. Like many harem protagonists, Jin is not allowed to have any interesting personality traits. Nagi pinwheels back and forth between haughty, cute, and peaceful, so much so that it's actually lampshaded, as she pretends to have a multiple personality for a while.
I understand that things get more interesting later on, but based on the first volume of this series, I can't see it appealing to a casual reader. As for fans of harem datesim-type manga, Kannagi should satisfy your desires.