Who can / can't use Power Ups in Mario world?

[Dorayaki]

＊Human: yes

＊Toads: yes

＊Kongs: firstly confirmed in Illumination movie, yes

＊Yoshis and possibly other dinos: cannot use the typical power ups, although they have a fruits as alternative power up source.

Super Bell serves as a weird example for most creatures including koopas to be able to transform into cats. But so far we've not seen other species use common power ups in general SMB scenarios, not sure if it's they don't want to, not actually able to or Kamek's magic is more useful. (Yes, Plessie also used Super Bell but is not able to use other common power ups, so Super Bell could be a very special exception among all items?

 

[Princess Mint]

In 3D Land enemies such as goomba or bullet bill sometimes have tanooki tails, and drop super leafs when defeated.

Enemies in Super Mario Maker can usually be enlarged by dragging a super mushroom to them.

Yoshi can use the Mega Mushroom and fire flower, among other things in Mario Kart, but items in Mario Kart work different than they do as power ups in other games, so this doesn't really contradict your findings.

It's also useful to note that powerups sometimes act differently depending on the game. Super Mushrooms in platformers usually let characters grow, but in rpgs they act as health restoring items instead. In some games the fire flower lasts until Mario gets hit, in other games it only works for a set amount of time. This is probably just for gameplay purposes but you could also imagine that this means that there are slightly different versions of power ups that are common in different locations.