The modeling of liquid spreading and penetration into fibrous materials requires a better understanding of the interactions of thin liquid films and small droplets with single fibers. The wetting properties of fibers may differ significantly from those of plane solid surfaces. Convex surfaces of fibers imply a positive Laplace pressure acting on the liquid-gas interface, This effect causes liquid film instability and hinders droplet spreading. Liquid films on fibers are stable when the destabilizing action of the Laplace pressure is balanced by liquid-solid adhesion. Equilibrium configurations of liquid droplets and films are determined by the competition between capillary and adhesion forces. A general analytical solution is presented for the equilibrium profile of the transition zone between a film and a droplet residing on a cylindrical fiber. A new equation for apparent contact angles on fibers is derived. Adhesion forces, including van der Waals and polar interactions, are expressed in terms of disjoining pressure. Explicit formulae for calculations of equilibrium droplet profiles, film thicknesses, apparent contact angles, and stability factors are presented in the form of expressions which include both the measurable geometrical parameters and the presumably known parameters of liquid-solid interactions, such as apolar and polar spreading coefficients, The method developed is applicable for analyses of apparent contact angles and film stability on fibers and other cylindrical surfaces, particularly nanofibers. It is shown that a transition from partial wetting to non-wetting may occur as the fiber diameter decreases. Depending on the fiber diameter, contact angles of water on hydrophobic carbon fibers may vary from 75 degrees (plane graphite surface) to 100-130 degrees (carbon nanotubes).