I've only just started on this with one game using my memory only before work, so not much has been added at all so far. I'd usually keep these things private to work on them further, but I thought I'd make this public in case of help anyone else can offer.
Status effects that remain after fights:
Pokémon: Paralysis, Poison, Burn
Final Fantasy 3: Poison, Darkness, Zombie, Imp, Float
Status effects that remain after fights, but can randomly disappear:
Pokémon: Sleep, Freeze
Status effects that disappear after fights, and can randomly disappear in-fight also:
Pokémon: Attraction, Confusion
Final Fantasy 3: Charm, Berserk, Safe, Reflect, Shell, Rage, Dance
Status Effects which change "the controller" of the afflicted:
FF3: Beserk, Confuse, Dance, Rage, Control, Zombie,
Statistics that can be raised/lowered whilst in a fight:
Pokémon: Speed, Attack, Defence, Attack Accuracy
Other things that appear erratically in games:
Alex Kidd: Telepathy