Vertically aligned carbon nanotube (CNT) forests may be used as miniature springs, compliant thermal interfaces, and shock absorbers, and for these and other applications it is vital to understand how to engineer their mechanical properties. Herein is investigated how the diameter and packing density within CNT forests govern their deformation behavior, structural stiffness, and elastic energy absorption properties. The mechanical behavior of low-density CNT forests grown by fixed catalyst CVD methods and high-density CNT forests grown by a floating catalyst CVD method are studied by in situ SEM compression testing and tribometer measurements of force-displacement relationships. Low-density and small-diameter CNT columns (fixed catalyst) exhibit large plastic deformation and can be pre-deformed to act as springs within a specified elastic range, whereas high-density and large-diameter CNT columns (floating catalyst) exhibit significant elastic recovery after deformation. In this work the energy absorption capacity of CNT forests is tuned over three orders of magnitude and it is shown that CNT forest density can be tuned over a range of conventional foam materials, but corresponding stiffness is similar to 10x higher. It is proposed that the elastic behavior of CNT forests is analogous to open-cell foams and a simple model is presented. It is also shown that this model can be useful as a first-order design tool to establish design guidelines for the mechanical properties of CNT forests and selection of the appropriate synthesis method.