Kryptonite is made up of the radioactive elements from the planet Krypton and seems to be deposited in small quantities all around Earth. Superman has had to carefully deal with it in its various forms throughout his world saving career. What about the non-radioactive chunks of Krypton that reached Earth? Has Superman discovered any, and if so, was he physically affected by it in any way?
Depending on the writing, non-radioactive materials from Krypton have no particular effect on him. Materials such as the metals, plastics and compounds which comprise his ship, are perfectly safe and react as normal metals and materials do on Earth.
The radioactive alloy which comprises Kryptonite is a very specific material whose origins vary widely depending on the origin story for the material.
The Silver Age Superman had a wide array of Kryptonites, with some having completely different effects on him, depending on their composition and color. Others had no effect on him at all, despite their radioactivity.
Blue Kryptonite, for example, was dangerous to Bizarro Superman, White Kryptonite killed all plant life and microorganisms. Gold Kryptonite would remove his powers permanently but had no other adverse effect.
The bottle city of Kandor, for example, was stolen by Brainiac before the radioactive event which converted the core of Krypton into an explosive material. So it did not expose the Kryptonians living on it when they were later brought to normal size.
In the Silver Age, Argo City, the home of Supergirl, survived the explosion of Krypton but part of the planet was covered with the radioactive material. Supergirl was sent to Earth as the Kryptonians slowly sickened and died.