A series of OVAs!
07th Expansion's original Higurashi no Naku Koro ni visual novel software revolved around murders that coincide with an annual festival in a quiet rural village. The software inspired two television anime series, several video anime projects, two live-action films, and manga adaptations by several artists.
The game publisher MangaGamer licensed the rights to translate the original visual novel software for personal computers, and it has released them in English. Funimation took over North American distribution of the first Higurashi television anime series from Geneon Entertainment and released the first DVDs in 2008. North America's Yen Press acquired the Higurashi manga for its Yen Plus anthology magazine and later for compiled book volumes.
Update: More background information added.
Update 2: The new series will launch on July 21.
Update 3: A preview site has opened for the new anime. The schedule for the four Blu-ray Disc/DVD volumes is as follows:
file.01 Batsukoishi-hen -Ki- July 21, 2011
file.02 Ayakashisenshi-hen -Do- September 22, 2011
file.03 Musubienishi-hen -Ai- (tentative) November 23, 2011
file.04 Yumeutsushi-hen -Raku- (tentative) January 25, 2012
The first volume will adapt the original software's Batsukoishi-hen storyline, while the remaining volumes will have all-new original stories.
There will be limited edition volumes with deluxe bonus extras, as well as regular edition volumes. The limited edition volumes will each have a "magical box" illustrated by Tomoyuki Abe (the character designer of the new anime), a tentatively titled "magical disc" CD with the ending theme and mini-drama, an original booklet with collaborative comics by famous creators, and a card for mail-away present. Buyers of all the volumes can receive a tapestry.
Ryukishi07/07th Expansion created the original story, and Toshifumi Kawase is again supervising the scripts. Hideki Tachibana is directing at Studio DEEN.
I'm somewhat excited for this despite there's no word for a season two of Umineko no Naku Koro Ni (despite S1 left a bad taste in my mouth). As far as I know, each "File" will be original expect for File 01 which will be based off of the visual novel.