Just a couple of mm thick, about 2-3 is enough. The fuselage barrel gets its strength from the large diameter: bending moments of the fuselage (and wing) get translated into tension and compression loads in the skin. The aircraft skin is the main load bearing structure.
It's the same principle as that for I-beams:they are that shape because the top and bottom plates carry the useful load, the middle bit is basically mainly there to keep them apart. If a beam is required for more load, increasing the distance between top and bottom has a quadratic effect on load level reduction. And the same principle that nature applies to bird bones: they are hollow, because the outer bit is the most effective.
The stringers and other structural helpers are mainly there to help keep the skin in shape, prevent buckling etc. Some older and/or smaller wings use a single, I-beam type spar for absorbing the ebnding moment, but most effective is the wing box shape: front spar, rear spar, top skin, bottom skin. It resists torsion best and reduces flutter, it also keeps the skin in better shape.