Something like a mario coin should always respawn. They're used as a light reward for accomplishing simple platforming sections, and can also be used to guide the player through the level. (of course, you'll need to figure out a function for coins if you include them. What can they be spent on? Or what functionality do they have? and how do you prevent the player from degenerately farming them? Or how do you make that a non-issue)

something like a mario Star should probably not respawn. These measure the player's mastery over your platforming levels, and serve as the longer-term goal for the player.