An open-cell carbon nanotube foam is made of a plurality of separated carbon nanotubes. The foam exhibits a Poisson's ratio substantially equal to zero, a compressibility of at least 85%, a recovery rate of at least 120 mm/min, a compressive strength of at least 12 MPa, a sag factor of at least 4, a fatigue resistance to no more than 15% permanent deformation when subjected to at least 1,000 compressive cycles at a strain of 85%, and/or a resilience of between 25% and 30%. The carbon nanotubes may be multiwalled carbon nanotubes that are aligned parallel to a thickness of a film comprising the foam.