Capillary forces arising during the evaporation of liquids from dense carbon nanotube arrays are used to reassemble the nanotubes into two-dimensional contiguous cellular foams. The stable nanotube foams can be elastically deformed, transferred to other substrates, or floated out to produce free-standing macroscopic fabrics. The lightweight cellular foams made of condensed nanotubes could have applications as shock-absorbent structural reinforcements and elastic membranes. The ability to control the length scale, orientation, and shape of the cellular structures and the simplicity of the assembly process make this a particularly attractive system for studying pattern formation in ordered media.