Two simple scratches. Sends the opponent flying a bit.
Forward + A
Winds up a bit and punches. Pretty quick move.
Dash + A
Bowser lunges his head forward. Bowser will fall to the ground with the momentum.
Down + A
Kneels down swings at your feet twice.
Up + A
Swings his fist above his head 180 degrees. Very strong and fast move.
Smash Forward + A
Turns around then unleashes a brutal headbutt. Extremely strong but insanely slow.
Smash Down + A
He spins around, hitting enemies with his spikes. Good for 7-10 hits.
Smash Up + A
He ducks then jumps up into the air, destroying any enemies near or above him. Computers almost always air-dodge near the beginning of the move.
A (When lying face up)
Bowser gets up and punches in a very wide arc that starts and can hit enemies behind him
A (When lying face down)
Bowser throws his body forwards and backwards.
A (When hanging off a ledge <100%)
Bowser very quickly climbs back up and just as quickly retracts into his shell and dashes forward and back, placing him in front of the ledge he just climbed back from.
A (When hanging off a ledge >100%)
Bowser heaves himself onto the edge and takes a swipe at nearby enemies.
He breathes fire much like using a Fire Flower item, however if you use it too long, the range of the attack will degrade until Bowser is left just breathing smoke.
Up + B
Whirling Fortress
On the ground, he spins around, damaging enemies. In the air, the initial attack will lift the opponent into the air, but if connected just right, the enemy will get sucked in for around 12-15 hits.
Down + B
Bowser Bomb
He jumps forward into the air and slams down crushing enemies underneath. In the air he'll just drop down where he is.
Forward + B
Koopa Klaw
He Swings forward attacking further enemies, but grabbing closer ones. To bite them press B. To throw them, press forward or backward. Forward throws will send them up a bit. Backwards throws will send the opponent flying quite a bit.
Flame Cancelling: In v.1.0, jumping, starting Bowser's flame breath, and then landing cancels the startup animation for the flame breath: Bowser will immediately starts breathing fire when he lands. This was fixed in later versions (Player's Choice, PAL/European), making v.1.0 more popular amongst Bowser players.