Air Zonk [ TurboGrafx-16 ] google +version+differences ★★★★★

Apidya [ Amiga ] google +version+differences

FIRE

ACTIVATE POWER-UP

A: hold and release: Stinger

Baraduke [ Arcade ] google +version+differences

FIRE

Arcade Database

Battle Mania 2: Daiginjo [ Genesis ] google +version+differences

Bio-Hazard Battle [ Genesis ] google +version+differences

Blazing Star [ Arcade ] google +version+differences ★★★★★

FIRE

BREAK

Arcade Database

Boogie Wings [ Arcade ] google +version+differences ★★★★★

FIRE

BOMB

Arcade Database

Carrier Air Wing [ Arcade ] google +version+differences ★★★★★

FIRE

SPECIAL WEAPON

Arcade Database

Cosmic Cop [ Arcade ] google +version+differences ★★★★★

Arcade Database

Cotton: Fantastic Night Dreams [ Arcade ] google +version+differences

Arcade Database

Cotton: Fantastic Night Dreams [ TurboGrafx-16 ] google +version+differences

Arcade Database

Cotton 100% [ SNES ] google +version+differences

Cotton 2: Magical Night Dreams [ Arcade ] google +version+differences ★★★★★

It's actually any 2 directions + A, and the directions pressed will affect the arc of the ball. And yes, you can make the ball big enough to cover the entire screen; do it fast enough, and it will prevent you from picking up any teapots, which gives you a special bonus (multiple tech sphere bonuses will appear). On later levels, those spheres are worth more points.
(tap same direction twice) + A - make a ball that you can grab and throw, you can make the ball bigger by hitting it with another ball.
back, forward + A - rapidfire
forward, back + A - triple shot
f, fd, d + A - arcing rapidfire downwards, from front to back
b, bd, d + A - arcing rapidfire downwards, from back to front (Cotton Boomerang only)
f, fu, u + A - arcing rapidfire upwards, from front to back
b, bu, u + A - arcing rapidfire upwards, from back to front (Cotton Boomerang only)
b, f, A, b, A, f, fd, d, A - rapidfire, triple shot, TWO arcing rapidfires (both upwards and downwards at the same time). f, fu, u, A in the end also works. (Cotton 2 only)
b, f, A, b, A, b, A, f, A - rapidfire, triple shot, TWO arcing rapidfires, then summon a dragon (Cotton Boomerang only). I just spam back + A then forward + A once the combo starts.
All the above combos will seal an enemy automatically, if they do the kill hit.
f, fd, d, db, b + B - grab AND seal the enemy (this is your default grab in Cotton Boomerang)
f, f, b - make Silk or Needle (the fairy and the living hat) take off or settle down on you. They automatically take off when you are hurt a lot. Cotton 2 only.
b, f, b, f + C - remove one of your magic slots, without producing a special attack. Cotton 2 only.
up, uf, f, fd, d, db, b, bu, u, down + A + B + C - suicide
Hold A - move faster
Hold A, double tap direction - dash in a direction (Cotton 2 only)
Hold A, release - summon a dragon (Cotton Boomerang only). This one has a long cooldown, but you can spam the combo that ends with a dragon, then do this hold move, and you can spam dragons nonstop. It's important because the dragon cancels incoming fire.

List of moves

Cotton 2 Saturn Manual
Arcade Database

Cotton 2: Magical Night Dreams [ Saturn ] google +version+differences ★★★★★

It's actually any 2 directions + A, and the directions pressed will affect the arc of the ball. And yes, you can make the ball big enough to cover the entire screen; do it fast enough, and it will prevent you from picking up any teapots, which gives you a special bonus (multiple tech sphere bonuses will appear). On later levels, those spheres are worth more points.
(tap same direction twice) + A - make a ball that you can grab and throw, you can make the ball bigger by hitting it with another ball.
back, forward + A - rapidfire
forward, back + A - triple shot
f, fd, d + A - arcing rapidfire downwards, from front to back
b, bd, d + A - arcing rapidfire downwards, from back to front (Cotton Boomerang only)
f, fu, u + A - arcing rapidfire upwards, from front to back
b, bu, u + A - arcing rapidfire upwards, from back to front (Cotton Boomerang only)
b, f, A, b, A, f, fd, d, A - rapidfire, triple shot, TWO arcing rapidfires (both upwards and downwards at the same time). f, fu, u, A in the end also works. (Cotton 2 only)
b, f, A, b, A, b, A, f, A - rapidfire, triple shot, TWO arcing rapidfires, then summon a dragon (Cotton Boomerang only). I just spam back + A then forward + A once the combo starts.
All the above combos will seal an enemy automatically, if they do the kill hit.
f, fd, d, db, b + B - grab AND seal the enemy (this is your default grab in Cotton Boomerang)
f, f, b - make Silk or Needle (the fairy and the living hat) take off or settle down on you. They automatically take off when you are hurt a lot. Cotton 2 only.
b, f, b, f + C - remove one of your magic slots, without producing a special attack. Cotton 2 only.
up, uf, f, fd, d, db, b, bu, u, down + A + B + C - suicide
Hold A - move faster
Hold A, double tap direction - dash in a direction (Cotton 2 only)
Hold A, release - summon a dragon (Cotton Boomerang only). This one has a long cooldown, but you can spam the combo that ends with a dragon, then do this hold move, and you can spam dragons nonstop. It's important because the dragon cancels incoming fire.