The series has the base of a very, very good story. But it feels half-baked to me - for many episodes there is little to explaination about the "curse". I felt ripped off by this later when it became interesting. It was as if the first few episodes were filler, pulling in the viewer with blood and gore and a small story - the curse, and other simple elements - then later deciding that it had a plot. If the writer/producers of this series were trying to hint at a story behind it all, then they failed.
However, there is some good to say about the series. It is definitely worth watching through the slow moments at the beginning. As the series progresses, the story becomes a bit more satisfying and we begin to see more sides of the story than "character 'insert name' goes crazy and kills 'insert name' and 'insert name' in 'insert name' location". Additionally, some of the scenes, when placed individually, are well thought out and gut wrenching.
For the reasons above, I give the story a 6. It has good roots, but needed to be expanded on more, and developed into a more concrete form. I give the art a 5, as it is rather generic. The sucks and weapon-hitting-target effects are very good, deserving a eight, although I did notice from time to time that the sounds were late (and I can do without the sound of rubber when someone is being choked). Characters are 7, I enjoyed it to a 9, and overall, in my eyes, Higurashi no Naku Koro Ni is worth a watch at a 8.
