Thought I'd start off with a full list of official BlazBlue related works. If I didn't pull the information in this guide from a direct source, then I got it from the Wikia, the Dustloop Forums, or the TVTropes Forum. Amatsumugi and Abyss of the Azure are also great resources.
BlazBlue: Calamity Trigger - Covers the events where Ragna first goes to Kagatsuchi until the timeloop is finally broken.
BlazBlue: Continuum Shift / BlazBlue: Continuum Shift Extend - Covers the events where Terumi smelts Noel into a Kusanagi and Ragna undoes it. Bonus stories cover Noel first entering the Academy and the Sector Seven collaboration with Relius. You can find detailed summaries of the bonus stories here.
BlazBlue: Chronophantasma / BlazBlue: Chronophantasma Extend - Covers the events where the Master Unit is summoned in Ikaruga. Bonus Stories cover Mai Natsume's life, Roy's fall, Kagura's Ikaruga War activities, and Bullet's search for truth.
BlazBlue: Centralfiction - Covers the end of Ragna's story.
XBlaze – Code: Embryo - Covers an alternate universe (that may be similar to BlazBlue mainline's 2050) where Takamagahara is about to be activated. Introduces Es.
XBlaze – Lost: Memories - Covers an alternate universe (that may be similar to BlazBlue mainline's 2090s). Probably stars Nine and Celica.
BlazBlue: Phase 0 - Covers AD 2200 Ragna traveling to the beginning of the Dark War and ultimately stopping the Black Beast for one year. This story is retold in Chronophantasma. Unofficially translated here.
BlazBlue: Phase Shift 1 - Covers Terumi claiming Kazuma Kval's body before the Dark War begins. Unofficially translated here.
BlazBlue: Phase Shift 2 - Covers the one year gap while the Black Beast is stopped. Focuses on the birth of Hakumen and the gathering of the Six Heroes. Unofficially translated here.
BlazBlue: Phase Shift 3 - Covers the creation of Take-Mikazuchi and the other first Nox Nyctores.
BlazBlue: Phase Shift 4 - Covers the creation of the remaining Nox Nyctores, the defeat of the Black Beast, and the fate of the Six Heroes.
BlazBlue: Spiral Shift - Covers Jin's time in the NOL and the Ikaruga War.
BlazBlue: Bloodedge Experience — Part 1 - Occurs before the Dark War (2070s-2090s), probably in an alternate universe. Focused on a new character Naoto, who'll meet Relius, Valkenhayn, and a Rachel-like Vampire named Raquel.
BlazBlue: Bloodedge Experience — Part 2 - Occurs before the Dark War (2070s-2090s), probably in an alternate universe. Continues Naoto's adventures.
BlazBlue: Calamity Trigger — Part 1 - Retelling of the events in Calamity Trigger.
BlazBlue: Calamity Trigger — Part 2 - Retelling of the events in Calamity Trigger.
BlazBlue: Continuum Shift — Part 1 - Retelling of the events in Continuum Shift.
BlazBlue: Continuum Shift — Part 2 - Retelling of the events in Continuum Shift.
BlazBlue: Remix Heart - School life during Noel's academy days. Focuses on a new character named Mai Natsume. This was scanlated and can be found on Batoto and other places.
BlazBlue: Variable Heart - A continuation of Remix Heart that takes place after the Ikaruga War. Mai is still the main character. An in progress scanlation can be found on Batoto and other places.
BlazBlue: Chimelical Complex - Covers Calamity Trigger and some of the short stories contained in the first Material Works.
BlazBlue - Retelling of Calamity Trigger. You can find a partial scanlation on Batoto and other places.
BlazBlue: Official Comics - Gag Manga.
BlazBlue: The Wheel of Fortune - Describes a failed attempt to end the Calamity Trigger timeloop. This timeloop results in the Tsubaki's death, the Black Beast being formed, and Jin becoming Hakumen. This is partially retold in Hakumen's story mode during Continuum Shift.
BlazBlue: Happy Trigger – Blue Drama Rebel One - Comedy Drama CD
BlazBlue: Happy Trigger – Blue Drama 2 Rebel Two - Comedy Drama CD.
BlazBlue: Happy Trigger Fan Disk - Comedy Drama CD that was a preorder bonus for Calamity Trigger in Japan.
BlazBlue ~Burudora Bangai Hen~ Tsubaki no Dokomade Iku no? - Comedy focused around Tsubaki that was a preorder bonus for Continuum Shift in Japan. You can find it subtitled here.
BlazBlue Phase 0 ~Prologue~ - Preorder bonus for Continuum Shift on PSP, this covers the beginning of Phase Shift 0. You can listen to it with subtitles here.
BlazBlue: Alter Memory - Retelling of Calamity Trigger and Continuum Shift. Twelve Episodes and localized in English by Funimation. You can watch it on hulu.
Radio: XBlaze - Radio program (like BlazBlue radio) that focused on XBlaze. It should still be on Nico Nico.
BlazBlue Material Collection - Material Collection for Calamity Trigger. It has a detailed timeline and one canon short story for every character. You can find the short story translations here here.
BlazBlue: Continuum Shift Material Collection - Has a short story called "Trigger Shift" that bridges Calamity Trigger and Continuum Shift. You can find a summary for it here
BlazBlue: Chronophantasma Material Collection
BlazBlue: Chronophantasma ~Story Maniacs~ Material Collection II
Arc 25th Anniversay Artbook - Contains two BlazBlue short stories: Scarlett Rose and Evergreen Eyes. You can find summaries of them here
BlazBlue Original Material Collection "Genesis of Blue Blaze" - 44-page artbook that was sold on Comic Market 80. It mostly contains concept art.
BlayzBloo: Super Melee Brawlers Battle Royale
BlazBlue Mobile Battle
BlazBlue: Battle Cards
BlazBlue: Battle × Puzzle
BlazBlue: Revolution Reburning
Eat Beat Dead Spike-san