What are some good, out-of-the-way uninhabited islands?

Key features must include:
-Rarely visited by man
-Relatively far from human habitation (far enough that people won't come check on it without good reason)
-Large and interesting enough to be worth visiting
-Climate that doesn't make visiting a living hell

A preferred but not required feature is:
-Not part of a protected park, nature area, or world-heritage site

Places like Auckland island south of NZ come to mind. Pic related.