I really like the cap powers in Super Mario 64. I wish powerups would go back to being temporary like that, at least in the 3D games. It ties in with how I want them to be more about exploration and less about point A-B.
As far as long-lasting powerups are concerned my favorite is the Cape Feather from SMW. I'd love to see it return honestly.
Also while Mega Mario is kinda "meh" to me in most games, I absolutely adore the Super Paper Mario incarnation. It really fits the style of the game while being a throwback to SMB at the same time. Plus the music rocks.
As for new power-ups, I think a Bowser Suit would be pretty neat. Kill any enemy in one stomp (even stuff like Chargin' Chucks) and breathe fire to burn away wood and reveal secret passages that the Fire Flower's fireballs are too weak to burn away. Pretty sure something like this was in a Mario Party game but not in the main series.
The mentioned Electric powerup would be neat too, but I'd actually rather it be exclusive to Luigi taking the place of the Fire Flower for Mario. It would be a nice nod to Superstar Saga.
Mole Mario has been done in a fangame, but I wouldn't mind seeing it implemented in an official game either. I'd also be interested in seeing the Hammer from Donkey Kong appear in a Super Mario platformer. Complete with a remix of the music from that game (I think this was in Treasure Tracker only with a pickaxe but can't say I've played that game)