According to the Kuroshitsuji website, there are 6 OVAs included in the DVD releases.
The Phantom Company plans a stage play for the poor children for it's 3rd anniversary since its foundation. But the original theater performers got into a ship accident on their way to London and won't make it in time for the presentation.
It is summer break and Keima intends to spend all his time on video games. An old acquaintance, the timid girl Tenri, comes back into the neighborhood - and apparently has a lost soul inside her. It is up to Keima and Elysia to unravel the secrets of her heart.
While on the surface Yuu Otosaka appears to be just another charming and intelligent teenager, he has a secret—he has the ability to slip into people's minds and fully control their body for five seconds at a time. Yuu has been using this skill for years to gain the highest grades, which allowed him to enter a prestigious high school.
Eli, Chihiro, and Miyako try to form a band but end up looking to Katsuragi for help. In the process they meet Kanon and become friends/ rivals.
Kanon spin-off OVA bundled with vol. 22 of the Kami nomi zo Shiru Sekai manga.
Short prologue OVA, bundled with manga volume vol.10.Elsie receives from Dokurou Skull, hell's branch chief of "counter measures", the task to go on earth and capture evil spirits that have escaped from hell.
Two OVA episodes are bundled as DVDs with each of volumes 6 and 7 of the manga.The first OVA is a prequel story written by the manga's author. Before the beginning of the main story, Rea and Chihiro have already met at a certain place: an outdoor hot-spring bath.The second OVA takes place after the series (effectively episode 14). The Furuya family finds a mysterious young girl hiding under the household temple.
Accel World EX is a OVA bundled with the Accel World simulation and action games. The Blu-ray OVA discs came with the PS3 limited edition versions and the DVD with the PSP limited edition versions.
Fate/Grand Order: First Order appears to be a prologue to upcoming events, which may actually form an anime (yet there is no info regarding such matters available as for today). The story is set in the Fate/stay night's Holy Grail War, and yet, it is not the one we all remember from the 2006 Deen version, nor Ufotable's UBW. So what route are we actually witnessing this time? A whole new one.