Kannagi starts off of an interesting premise –Mikuriya Jin, a high school student, carves a sculpture from a holy tree which later turns into the goddess of the area, Nagi. Because people nowadays do not believe in gods as much and because her tree was cut, Nagi is very weakened, and must get rid of roaches –erm, impurities. So far, so good. If only they'd actually follow that plot.
Unfortunately, Kannagi seemed to have decided that that is not a successful money bringing strategy, and resorted to your typical ecchi comedy/slice of life/high school anime subplots. You know them; Nagi living with Jin, pretending to be his half-sister (giving a chance to reuse the same over-repeatedly gag of other characters wondering whether they really act towards each other as siblings); the love triangle-square-pentagon whatever (after the presumably gay relationship between Jin and his best friend it really isn't clear anymore); and of course, the obligatory episodes of said genre –bra buying, karaoke singing and so on. Now these might seem exciting if you're new to this kind of anime; sadly, after seeing 20+ series of the same sort, you really cannot help but blame Kannagi for the lack of innovation. What about romance then? Pff, that's really nothing but a lame excuse to bring lots and lots of fanservice. Because why not?
In the end, I'd only recommend this series to people who are generally new to anime and haven't experienced all the cliches this certain genre carries with it.