Metal Gear Solid-related:
-Akebi Sasaki from Girls und Panzer got pulled into the MGS universe by a Philosophers' experiment gone awry. She was brainwashed and trained by them and eventually became the legendary hero known as The Boss.
-Cecile's memories of living in France are fake, she was actually created by Strangelove at the very lab she escaped from. She's actually an altered genetic clone of The Boss, produced as an offshoot of the Les Enfants Terribles program. Cecile has combat abilities far beyond any other human being, she just doesn't know it because she's never had to use them. She was given the codename Liquid Boss upon creation, and has a genetically inferior brunette sister codenamed Solid Boss. After narrowly avoiding the destruction of MSF, Cecile traveled to France, but was shocked to find that the house she remembered growing up in did not exist. Strangelove then appeared with Solid Boss by her side and explained what she really was, then they tried to capture her. They failed miserably, and Cecile decided to dedicate her life to fighting the Patriots and Cipher.
-Portable Ops is absolute canon and not uncertain in any way.
Final Fantasy VII-related:
-The Lifestream was created by GNR as she died in order to bring the planet back to life.
-The part of Rei that wasn't Yui or Lilith re-materialized out of the LCL as a complete individual and later became Shinji's wife. They formed a tribe called the Shin-RA (Shin standing for Shinji, RA being an abbreviation of Rei Ayanami. Thousands of years later their descendants formed a mega-conglomerate of the same name.
-Materia are miniaturized versions of angel cores.
-The Cetra are members of the First Ancestral Race who came to earth to investigate after they detected the death of GNR.
-Jenova is a corrupted Seed of Life that was being hunted by the FAR before it crashed into earth.
-Genesis is the last descendent of a tribe called the Shinsuka, which was formed by an illegitimate child Shinji and Asuka conceived during an affair.
-After the end of Persona 4 Arena, Labrys and Aigis travel back to the lab where Labrys was created, and together they rebuild all of the 5th-generation Anti-Shadow Weapons that Labrys had been forced to destroy as part of her training. Labrys and Number 24 make up and get back together.
-The main character of Persona 3 is actually a male shiny Gardevoir desperately trying to pass himself off as a human so he can avoid being captured and used in Pokemon battles.
-Yukiko Amagi is secretly a death metal junkie. She has a secret soundproof room at her family's inn where she can listen to it without being discovered.
-Ryotaro Dojima is actually a persona-user and a member of the Shadow Operatives. He never mentions this to Yu because it's classified and he doesn't know Yu can also use a persona.
These are just a few, I'll have more later. What's your video game headcanon?