This topic evokes some strong emotions for me. Y'know, the sort of thing my sons and I can stay up 'till 3am discussing...
A few $.02 thoughts/random examples.
Reboots: Some 'historical' heroes (The Three Musketeers and Zorro) are so episodic in nature that they really lend themselves to reboots. Also true with superheroes in comics, right? (Google Umberto Eco's essay "The Myth of Superman" for a deeper dive)
My personal favorites are the ones that actually do end up moving the character along through life-stages and creating different generations of the legend; so, like, in those above examples, I would first point to—one of my stranded-on-an-island-movies—"The Mask of Zorro" (1988), or "The Musketeers" (2014-2016, BBC television series, 30 episodes). But, like everyone has said, for every one of those, how many cash grabs do we have to sit through?
Remakes: These tend to go down less well with me. This is especially true of those that have original works that are so well done nothing thereafter really even has a chance of coming close (e.g., IMO, "Willy Wonka and the Chocolate Factory", "Ghostbusters", "Robocop") so what you end up with are either 'cover band' efforts or outright abominations.
On the other hand, someone mentioned the latest Dune. IMO, Some remakes are of such quality that I would consider them all-time greats in their own right. Dune will be there, I think. When it's done.