Kirby's Falcon Hat gives Kirby 64 Falcon Punch - same startup, same damage [20%], etc.
Fox hat gives Kirby Fox Illusion.
Samus hat gives Kirby screw attack [or missiles].
Falco hat gives Kirby Falco's reflector [with 3.Q properties, or if Falco's reflector gets reverted, 4.0 properties]. Alternatively, Kirby gets slow lasers.
ZSS hat gives Kirby Flip Jump, and the flip jump is invincible for most of the duration [most = at least half].
Luigi hat gives Thunderbrand with super armor.
Peach hat gives Kirby turnip pulling powers.
ICs hat gives Kirby squall hammer... but with Kirby's own hammer and half the normal power of Kirby's side+b.
Jiggs hat gives Kirby pound, rest, or a grab-cancellable sing [Jiggs is airborne so much a grab cancel isn't that practical].
Zelda hat gives Kirby Zelda's ftilt.
Diddy Kong hat gives Kirby Diddy Kong's sunglasses and he pulls bananas.
Wario's hat gives Wario waft.
Charizard hat gives blast burn [or rock smash].
Bowser Hat gives Kirby blue fire breath that deals 4% per hit but wears out kinda quick.
Link hat gives the old fire ice electric light arrows.
Pikachu hat gives t-jolts that also have a paralyze effect.
Sonic hat gives Kirby a homing attack that's interruptible for the entire duration by homing attack, and Kirby says "You're too slow!" in his adorable voice every time he presses B [IDK if that's even possible, but if so, if you only took one of my hat ideas, make this happen].
Yoshi hat gives Kirby Yoshi Eggs.
GnW hat gives judgement, but only 6-8. You can hold B during Judgement once only for a 9, but you lose the hat if you do so [probably WAY too overpowered, but it sounds awesome.]
Ivysaur hat gives Leaf Storm in the air, and on the ground it's vine whip [dthrow combos?]
Olimar hat gives whistle with a generous super armor effect [at least as good as Brawl]. Using the whistle then causes Pikmin to return to Olimar, knocking them off Kirby [making this hat very useful in MU and stopping Kirby from being camped hard].
Lucario hat is affected by aura only positively [no effect until whenever Lucario's aura would make his damage multiplier beyond 1.0, then it follows the multiplier exactly].