Jumping is the most basic ability present in platformers. A jump will allow Tux to reach four tiles in height.
Running is an automatic action that gets activated when Tux is walking in the same direction for a certain amount of time. When Tux is running he is able to jump five tiles high instead of just four.
Milestone 1 used a dedicated run button, since Milestone 2 it's automatic.
Ducking can be used to slide down small, one tile high holes as big Tux or to avoid projectiles which are shot one tile above ground.
Walking into or standing next to carriable objects while holding the ACTION key allows Tux to carry the object around. Releasing the ACTION key while walking results in Tux throwing the object. Doing so while standing still results in Tux simply dropping the object right next to him.
The buttjump is an ability that lets Tux crush boxes from above and destroy some badguys that cannot be harmed by a normal jump. It is performed by jumping up into the air and then pressing the DOWN key while in the air. It takes Tux a small amount of time to jump back onto his feet to get back to normal
The backflip is a special jump which gives Tux some extra height compared to a normal jump. It requires that Tux comes to a full stop and turns around.
When in water, Tux can move and turn in all directions with his movement speed being momentum based.
Instead of jumping, Tux can gain a small boost which lets him swim subsequently faster if used repetitively.
The behaviour of the fireflower is that it gives Tux the ability to spit bouncing fire bullets. Most badguys are killed when being struck by a fire bullet.
Any subsequent fireflowers that Tux takes increase the amount of fire bullets that can be on the screen at the same time, but do not increase the amount of hits Tux can take.
The iceflower will give Tux the ability to shoot ice bullets. Ice bullets will not bounce like fire bullets, but will shoot out in a straight path towards the enemy. When the ice bullet hits an enemy it will freeze him for a short time, if the enemy is actually freezable.
Any subsequent iceflowers that Tux takes increase the amount of ice bullets that can be on the screen at the same time, but do not increase the amount of hits Tux can take.
The airflower grants Tux the ability to jump much higher and run much faster. Additionally, holding down the JUMP key after a jump will allow Tux to glide for a couple of seconds.
Any subsequent airflower that Tux takes increase the amount of time Tux can glide, but do not increase the amount of hits Tux can take.
The earthflower will give Tux the ability to turn into a stone version of himself for a short amount of time. When turned to stone, Tux is invulnerable to all types of damage, but cannot move during that.
In dark areas the eartflower will also provides a small cone of light.
Any subsequent earthflower that Tux takes increase the amount of time Tux will remain in his stone form, but do not increase the amount of hits Tux can take.
An white star will turn Tux invincible for about 14 seconds, visualized by white sparks surrounding him.
The Tuxdoll grants Tux 100 extra coins.
Before Milestone 2, a Tuxdoll granted one extra life.
The blowflyer or BalloonTux action should be a temporary limited action in which Tux fills his body with air (helium?!) and is thus able to fly for a short time, i.e. as long as he can go without breathing. The end of the flight should be announced by Tux changing color and catching for air.
Perhaps there could be a hidden “pump” in each level, which tux could pump himself up with.
Tux will be able to make use of smooth terrain by using the slide action. By using the slider action Tux will jump on its belly and thus slide speedy down the hill. Terrain that is formed like a ramp should allow him to make huge jumps, which would be impossible without the slide action. While sliding downhill Tux shall be invulnerable by normal enemies, however special enemies with spikes or so, might still be able to stop him.
Exact details on how the sliding will work have to be worked out, but it might get a rather central role in gameplay.
Somewhat related, you could have icy platforms that when running on it is much harder to stop/change-direction (i.e. you could slide off the edge accidently) that require you to be extra careful.. these could appear on later harder levels. If these aren't flat, you get what is shown in the above picture, which you could slide down instead.
We'd probably need tile-based friction to make this work well. Holding “duck” while moving above a certain speed (or on a slope) will reduce Tux's friction by a large factor (4?) and make him slide as illustrated in the above picture. He'll be able to kill/stun certain enemies this way, but some (like the spiky ones) will damage and stop him.
Once in the air, Tux should be allowed to flap with his wings. They are not enough to let him fly, but should allow him to get some additional air-time (like a small double-jump).
When jumping from a great height, Tux should have his beak facing down, like a dive. It would work well with the swim ability.