What materials are close to soundproof?
If you mean preventing the transmission of sound to another space (rather than deadening reflections within a room), then it depends on cost and room available. Almost anything, if thick enough, will block sound. A hill of dirt does a great job of blocking almost any sound short of an earthquake, for instance. In more practical terms (if you don’t want to live in a cave), dense (as in lead or stone) multilayer barriers with dead space and no physical connection between the layers will block virtually all transmission.
Staggered studs and rubber isolation barriers help a lot if you’re talking about conventional building materials, especially with multiple layers of stone, brick or drywall, but really only qualify for sound reduction, not being soundproof. Any penetrations of the walls, floor or ceiling (doors, windows, electrical, plumbing, heat or A/C) would lessen the effectiveness of the acoustic barrier. It’s tough!
The best acoustic insulation is a vacuum (if you want actual soundproof construction), but that also requires isolating the two sides from each other at the edges (side, floor and ceiling) and ideally would include both floor and ceiling having a similar vacuum construction, assuming that you’re talking about using this in a occupyable room.
Here’s a site that explains some issues and calculations pretty well (click around the site links for more pages).