1. Corpse Party (including Blood Covered / Repeated Fear versions)*
2. Corpse Party: Book of Shadows
3. Corpse Party: Sweet Sachiko’s Hysteric Birthday Bash**
4. Corpse Party: Blood Drive
5. Corpse Party 2: Dead Patient
* The PSP version (
Repeated Fear) added some updated sprite art (which are used in the other games), professional voice acting, and CGs of some events. The version sold on GOG/Steam use the old indie art and voice acting,
but there is a mod that adds the PSP sprites and voice acting into the PC version (no CGs though, sadly).
** aka Hysteric Birthday 2U. This one is a bit of a tongue-in-cheek take on the series, but is still relevant. IIRC it can be skipped if you wish.
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[edit: Kaaedus can tell you about the anime - read the next post :D]
I also haven't read any of the manga, but supposedly
Another Child is a spin-off and so would have its own unique content. No idea where it fits in exactly, other than it "taking place during the events of Corpse Party". So... at least play the first game before reading, if you're interested.