In Super Mario Bros. there's really no need for a favourite, each one is a straight upgrade, Mushroom -> Fire Flower -> Star; and Super Mario Bros. 2 wasn't particularly power-up oriented. Super Mario Bros. 3 was the first one where there were actual points at which you'd have to choose which power-up to use, in which my favourite is definitely the frog suit. Besides my love of frogs, making my least favourite kind of level(fuck swimming) easier is just plain sweet. That's not to say it's an easy choice, though, the tanuki suit is wicked fun. In Super Mario World, of course it's the cape, for all the same reasons as it was the tanuki suit in Super Mario Bros. 3.
In the 3D games it's a bit harder to pick a favourite item since you generally need to use a specific one in order to do something, less like weapons and more like level-specific gameplay changes, or sometimes the challenge is in doing what needs to be done before the item's time limit runs out. I'd say my favourite in Super Mario 64 is the Wing Cap just because the others don't actually change gameplay much; my favourite in Super Mario Sunshine is the Hover Nozzle, even if it doesn't really count as a power-up since it's the default, I find it way more fun to use than the other nozzles; and my favourite in Super Mario Galaxy is the Ice Flower, because skating is the second coolest way to get around in that game behind flying through space.
I don't know about the NSMB games, but I know the Penguin Suit is fucking awesome. I'll never report back on my favourite SM3DL power-up because I will never play it more.
Rock Mushroom (Super Mario Galaxy 2)
Boomerang Flower (Super Mario 3D land)
Penguin Suit (SMBW)
Ice Flower (SMBW)
Boo Mario (SMG)
Blue Koopa shell(NSMB)
Attack Frog (Mario Party Advance)